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    "# Dynamical Critical Exponents in the 2D Ising Model\n",
    "\n",
    "Critical slowing down makes equilibrium sampling progressively harder as a continuous transition is approached. At the Onsager point, the integrated autocorrelation time of the magnetization scales as\n",
    "$$\\tau_{\\mathrm{int}}(L) \\propto L^z,$$\n",
    "so the dynamical critical exponent $z$ quantifies how fast the decorrelation cost grows with lattice size [[1]](bibliography.md).\n",
    "\n",
    "This notebook compares random-site Metropolis dynamics with the Wolff cluster update using the same measurement target as `scripts/ising/measure_z.py`. The central observable is the slope of $\\tau_{\\mathrm{int}}(L)$ on log-log axes: Metropolis remains diffusion-limited ($z \\approx 2.17$), while Wolff drastically reduces critical slowing down. In the cluster-step units used throughout this notebook, $z^{\\mathrm{cs}} \\approx 0.5$ (asymptotic value; fits at $L = 16$–$128$ yield $z^{\\mathrm{cs}} \\approx 0.40$); normalised to equivalent-sweep units, $z^{\\mathrm{sw}} \\approx 0.25$ [[2, 3]](bibliography.md).\n",
    "\n",
    "The analysis is organized in four parts:\n",
    "1. Physical mechanism: why local and cluster dynamics produce different scaling slopes, and what the unit convention means.\n",
    "2. Data ingestion: load cached script output (or run a small fallback demo).\n",
    "3. Uncertainty-aware fitting: estimate $z$ in log-log space with diagnostics and confidence intervals.\n",
    "4. Interpretation: connect numerical slopes to sampling strategy and the difference between algorithmic efficiency and physical dynamics."
   ]
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    "## Why the slopes differ\n",
    "\n",
    "Local Metropolis updates propose one spin-flip at a time, so relaxation near $T_c$ is diffusive: the correlation length $\\xi$ diverges as the transition is approached, and the system must cross free-energy barriers through small local moves. This leads to $z \\approx 2.17$ for the 2D Ising random-site Metropolis [[3]](bibliography.md).\n",
    "\n",
    "Wolff instead grows a cluster from a random seed by bonding same-sign nearest neighbours with probability\n",
    "$$P_{\\mathrm{add}} = 1 - e^{-2\\beta J},$$\n",
    "a choice derived from the Fortuin–Kasteleyn random-cluster representation [[4]](bibliography.md) that guarantees detailed balance with a 100% acceptance rate. Flipping a whole correlated domain in one move matches the scale of critical fluctuations and suppresses the diffusive bottleneck, yielding $z^{\\mathrm{cs}} \\approx 0.5$ in cluster-step units [[2, 3]](bibliography.md).\n",
    "\n",
    "### Defining $\\tau_{\\mathrm{int}}$ and the update unit\n",
    "\n",
    "$\\tau_{\\mathrm{int}}$ counts the number of update steps required to generate one statistically independent sample. The meaning of \"one step\" differs between algorithms:\n",
    "\n",
    "| Algorithm | Work per step |\n",
    "|-----------|---------------|\n",
    "| Random-site Metropolis | one spin-flip attempt |\n",
    "| Wolff cluster | one cluster flip of $\\langle C \\rangle$ spins — 100% acceptance rate |\n",
    "\n",
    "Counting raw step numbers treats a Wolff step near $T_c$ — which flips an $O(L^{7/4})$-spin cluster — as equivalent to a single Metropolis attempt. Comparing raw $\\tau_{\\mathrm{int}}$ values directly is therefore **misleading**.\n",
    "\n",
    "### Normalisation to sweep-equivalent units\n",
    "\n",
    "The standard fix is to express both algorithms in units of one $L^2$-flip-attempt sweep. Metropolis is already in this unit; Wolff requires reweighting by the mean cluster fraction:\n",
    "$$\\tau^{\\mathrm{sw}}_{\\mathrm{Wolff}} = \\tau^{\\mathrm{cs}}_{\\mathrm{Wolff}} \\times \\frac{\\langle C \\rangle}{L^2}.$$\n",
    "\n",
    "At $T_c$, the mean Wolff cluster size scales as $\\langle C \\rangle \\sim \\chi \\sim L^{\\gamma/\\nu} = L^{7/4}$, using the exact 2D Ising exponents $\\gamma = 7/4$ and $\\nu = 1$. Substituting into the sweep-equivalent relation:\n",
    "$$z^{\\mathrm{sw}} = z^{\\mathrm{cs}} + \\frac{7}{4} - 2 = z^{\\mathrm{cs}} - \\frac{1}{4}.$$\n",
    "With $z^{\\mathrm{cs}} \\approx 0.5$, this gives $z^{\\mathrm{sw}} \\approx 0.25$ — a 9× reduction relative to Metropolis, but **not** zero. Wolff drastically reduces critical slowing down; it does not eliminate it.\n",
    "\n",
    "For the full work-normalisation derivation, ISS (independent-samples-per-second) comparison, and temperature-resolved data, see the companion [Wolff Efficiency](wolff_efficiency.ipynb) notebook.\n",
    "\n",
    "### Units used in this notebook\n",
    "\n",
    "This notebook reports $\\tau_{\\mathrm{int}}$ in **cluster-step units** throughout, matching the output of `scripts/ising/measure_z.py`. The measured Wolff slope is therefore the cluster-step exponent $z^{\\mathrm{cs}} \\approx 0.5$ (asymptotic value; fits at $L = 16$–$128$ yield $z^{\\mathrm{cs}} \\approx 0.40$). The sweep-equivalent exponent is $z^{\\mathrm{sw}} = z^{\\mathrm{cs}} - 1/4 \\approx 0.25$."
   ]
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   "source": [
    "## Load or compute data\n",
    "\n",
    "This notebook needs $\\tau_{\\mathrm{int}}(L)$ measurements at $T_c$ for random-site Metropolis and Wolff updates across multiple lattice sizes. It first searches for precomputed results at `../results/ising/dynamic_exponent_z.npz`.\n",
    "\n",
    "If the cache exists, the notebook loads it directly. When per-size replicate arrays (`tau_metro_samples`, `tau_wolff_samples`) are present, medians are used as central values and 16–84% percentile bands are shown as error bars. If those fields are absent (legacy single-trajectory cache), the notebook still runs and treats each size as a single-point estimate with no error bars.\n",
    "\n",
    "If the cache is missing, the notebook runs a small inline fallback (sizes 16, 24, 32 with short trajectories). The fallback is only for pipeline validation and quick plotting; it is not a publication-quality estimate of $z$.\n",
    "\n",
    "To generate high-quality cached data with uncertainty bands, run:\n",
    "```bash\n",
    "python scripts/ising/measure_z.py --sizes 16 32 48 64 96 128 --n-seeds 10\n",
    "```\n",
    "This writes `../results/ising/dynamic_exponent_z.npz` with 10 independent seed replicas per (algorithm, $L$) point, matching the replication depth of the reference notebooks."
   ]
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     "text": [
      "Loaded pre-computed data from ../results/ising/dynamic_exponent_z.npz: 6 Metropolis sizes (replicates per size: 10), 6 Wolff sizes (replicates per size: 10).\n"
     ]
    }
   ],
   "source": [
    "from __future__ import annotations\n",
    "\n",
    "import os\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "from utils.exceptions import ZeroVarianceAutocorrelationError\n",
    "from utils.physics_helpers import calculate_autocorr\n",
    "\n",
    "TC_ISING = 2.0 / np.log(1.0 + np.sqrt(2.0))\n",
    "NPZ_PATH = '../results/ising/dynamic_exponent_z.npz'\n",
    "PALETTE = {'metro': '#4878CF', 'wolff': '#D65F5F'}\n",
    "\n",
    "\n",
    "def estimate_tau(update: str, size: int, meas_steps: int, seed: int) -> float:\n",
    "    from models.ising_model import IsingSimulation\n",
    "    from utils.system_helpers import convergence_equilibrate\n",
    "\n",
    "    sim_r = IsingSimulation(size=size, temp=TC_ISING, update=update, init_state='random', seed=seed)\n",
    "    sim_o = IsingSimulation(size=size, temp=TC_ISING, update=update, init_state='ordered', seed=seed)\n",
    "    convergence_equilibrate(sim_r, sim_o, chunk_size=100, max_steps=10000)\n",
    "    mags, _ = sim_r.run(n_steps=meas_steps)\n",
    "\n",
    "    try:\n",
    "        _, tau_int = calculate_autocorr(time_series=np.asarray(mags, dtype=float))\n",
    "    except ZeroVarianceAutocorrelationError:\n",
    "        tau_int = float('nan')\n",
    "\n",
    "    return float(tau_int)\n",
    "\n",
    "\n",
    "def _shape_to_samples(arr: np.ndarray) -> np.ndarray:\n",
    "    \"\"\"Return a 2D (n_size, n_rep) view for uncertainty handling.\"\"\"\n",
    "    a = np.asarray(arr, dtype=float)\n",
    "    if a.ndim == 1:\n",
    "        return a[:, None]\n",
    "    return a\n",
    "\n",
    "\n",
    "_cache_ok = False\n",
    "if os.path.exists(NPZ_PATH):\n",
    "    data = np.load(NPZ_PATH)\n",
    "    required = {'L_metro', 'tau_metro', 'L_wolff', 'tau_wolff', 'Tc'}\n",
    "    if required.issubset(set(data.files)):\n",
    "        L_metro = np.asarray(data['L_metro'], dtype=float)\n",
    "        tau_metro = np.asarray(data['tau_metro'], dtype=float)\n",
    "        L_wolff = np.asarray(data['L_wolff'], dtype=float)\n",
    "        tau_wolff = np.asarray(data['tau_wolff'], dtype=float)\n",
    "        Tc = float(data['Tc'])\n",
    "\n",
    "        # Optional replicate/sample arrays for uncertainty-aware aggregation.\n",
    "        tau_metro_samples = _shape_to_samples(data['tau_metro_samples']) if 'tau_metro_samples' in data.files else tau_metro[:, None]\n",
    "        tau_wolff_samples = _shape_to_samples(data['tau_wolff_samples']) if 'tau_wolff_samples' in data.files else tau_wolff[:, None]\n",
    "\n",
    "        # Robust summary across replicates if available.\n",
    "        tau_metro_med = np.nanmedian(tau_metro_samples, axis=1)\n",
    "        tau_wolff_med = np.nanmedian(tau_wolff_samples, axis=1)\n",
    "        tau_metro_p16 = np.nanpercentile(tau_metro_samples, 16, axis=1)\n",
    "        tau_metro_p84 = np.nanpercentile(tau_metro_samples, 84, axis=1)\n",
    "        tau_wolff_p16 = np.nanpercentile(tau_wolff_samples, 16, axis=1)\n",
    "        tau_wolff_p84 = np.nanpercentile(tau_wolff_samples, 84, axis=1)\n",
    "\n",
    "        n_rep_m = tau_metro_samples.shape[1]\n",
    "        n_rep_w = tau_wolff_samples.shape[1]\n",
    "        print(\n",
    "            f'Loaded pre-computed data from {NPZ_PATH}: '\n",
    "            f'{len(L_metro)} Metropolis sizes (replicates per size: {n_rep_m}), '\n",
    "            f'{len(L_wolff)} Wolff sizes (replicates per size: {n_rep_w}).'\n",
    "        )\n",
    "        _cache_ok = True\n",
    "    else:\n",
    "        print(f'Cache at {NPZ_PATH} is missing expected keys; running inline fallback.')\n",
    "\n",
    "if not _cache_ok:\n",
    "    print(\n",
    "        'Pre-computed data not found. Running inline demo '\n",
    "        '(sizes 16, 24, 32; non-publication-quality).'\n",
    "    )\n",
    "    sizes = [16, 24, 32]\n",
    "    L_metro = np.asarray(sizes, dtype=float)\n",
    "    L_wolff = np.asarray(sizes, dtype=float)\n",
    "\n",
    "    tau_metro = np.asarray(\n",
    "        [estimate_tau(update='random', size=size, meas_steps=2500, seed=idx * 100) for idx, size in enumerate(sizes)],\n",
    "        dtype=float,\n",
    "    )\n",
    "    tau_wolff = np.asarray(\n",
    "        [estimate_tau(update='wolff', size=size, meas_steps=800, seed=idx * 100 + 1) for idx, size in enumerate(sizes)],\n",
    "        dtype=float,\n",
    "    )\n",
    "\n",
    "    tau_metro_samples = tau_metro[:, None]\n",
    "    tau_wolff_samples = tau_wolff[:, None]\n",
    "    tau_metro_med = tau_metro.copy()\n",
    "    tau_wolff_med = tau_wolff.copy()\n",
    "    tau_metro_p16 = tau_metro.copy()\n",
    "    tau_metro_p84 = tau_metro.copy()\n",
    "    tau_wolff_p16 = tau_wolff.copy()\n",
    "    tau_wolff_p84 = tau_wolff.copy()\n",
    "\n",
    "    Tc = TC_ISING\n",
    "    print(f'Computed fallback data at T_c = {Tc:.6f} for sizes {sizes}.')"
   ]
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    "## Scaling fit with diagnostics and uncertainty\n",
    "\n",
    "We fit the power law\n",
    "$$\\tau_{\\mathrm{int}}(L) = A L^z$$\n",
    "by linear regression in log space:\n",
    "$$\\log \\tau_{\\mathrm{int}} = z\\,\\log L + \\log A,$$\n",
    "where $\\tau_{\\mathrm{int}}$ is the integrated autocorrelation time of the magnetization time series and $A = A(T_c)$ is a non-universal prefactor.\n",
    "\n",
    "### Primary estimate: per-seed z distribution\n",
    "\n",
    "With 10 independent seed replicas per $(L, \\text{algorithm})$ point, the most direct way to quantify uncertainty in $z$ is to fit independently for each seed and collect the resulting distribution:\n",
    "$$z_s = \\text{slope of } \\log \\tau_{\\mathrm{int}}^{(s)} \\text{ vs } \\log L, \\quad s = 1, \\ldots, N_{\\mathrm{seeds}}.$$\n",
    "The reported $z$ and its 16–84% interval come from the median and percentiles of $\\{z_s\\}$. This captures run-to-run variability in $\\tau_{\\mathrm{int}}$ directly, rather than relying on OLS residuals over only six lattice sizes.\n",
    "\n",
    "### Reference curve: OLS fit on per-size medians\n",
    "\n",
    "An OLS fit on the per-size median values provides a smooth reference line and 95% confidence band for the scaling plot. Per-size uncertainty is shown as error bars (16–84% across seeds at each $L$).\n",
    "\n",
    "Both estimates are printed in the summary table below the figure."
   ]
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",
      "text/plain": [
       "<Figure size 1300x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "z from per-seed fit distribution (primary estimate):\n",
      "----------------------------------------------------------------------\n",
      "  Metropolis     z = 2.065  (16–84%: 1.998 – 2.161)  n_seeds = 10\n",
      "  Wolff (cs)     z = 0.405  (16–84%: 0.397 – 0.416)  n_seeds = 10\n",
      "\n",
      "OLS fit on per-size medians (reference line on left panel):\n",
      "----------------------------------------------------------------------\n",
      "  Metropolis     z = 2.119  (OLS SE: 0.030,  R² = 0.9992)\n",
      "  Wolff (cs)     z = 0.404  (OLS SE: 0.014,  R² = 0.9954)\n",
      "\n",
      "Note: Wolff z is in cluster-step units; sweep-equivalent z ≈ z_cs − 0.25.\n"
     ]
    }
   ],
   "source": [
    "def fit_loglog(L: np.ndarray, tau: np.ndarray) -> dict[str, float | np.ndarray]:\n",
    "    \"\"\"Fit log(tau) = z*log(L) + b and return diagnostics.\"\"\"\n",
    "    valid = np.isfinite(L) & np.isfinite(tau) & (L > 0) & (tau > 0)\n",
    "    x = np.log(np.asarray(L[valid], dtype=float))\n",
    "    y = np.log(np.asarray(tau[valid], dtype=float))\n",
    "    n = x.size\n",
    "    if n < 3:\n",
    "        raise ValueError('Need at least 3 valid points for log-log fit.')\n",
    "\n",
    "    z, b = np.polyfit(x, y, 1)\n",
    "    yhat = z * x + b\n",
    "    resid = y - yhat\n",
    "    rss = float(np.sum(resid**2))\n",
    "    tss = float(np.sum((y - y.mean())**2))\n",
    "    r2 = 1.0 - rss / tss if tss > 0 else np.nan\n",
    "\n",
    "    sxx = float(np.sum((x - x.mean())**2))\n",
    "    sigma2 = rss / (n - 2)\n",
    "    z_se = float(np.sqrt(sigma2 / sxx))\n",
    "    b_se = float(np.sqrt(sigma2 * (1.0 / n + (x.mean() ** 2) / sxx)))\n",
    "\n",
    "    return {\n",
    "        'z': float(z), 'b': float(b), 'A': float(np.exp(b)),\n",
    "        'z_se': z_se, 'b_se': b_se, 'r2': float(r2),\n",
    "        'x': x, 'y': y, 'yhat': yhat, 'resid': resid,\n",
    "        'n': int(n), 'sigma': float(np.sqrt(sigma2)),\n",
    "        'x_mean': float(x.mean()), 'sxx': sxx,\n",
    "    }\n",
    "\n",
    "\n",
    "def mean_band(fit: dict, x_new: np.ndarray) -> tuple[np.ndarray, np.ndarray, np.ndarray]:\n",
    "    \"\"\"OLS 95% confidence band for the mean log prediction, transformed to linear scale.\"\"\"\n",
    "    y_pred = fit['z'] * x_new + fit['b']\n",
    "    se_mean = fit['sigma'] * np.sqrt(1.0 / fit['n'] + ((x_new - fit['x_mean']) ** 2) / fit['sxx'])\n",
    "    return np.exp(y_pred), np.exp(y_pred - 1.96 * se_mean), np.exp(y_pred + 1.96 * se_mean)\n",
    "\n",
    "\n",
    "# ---------------------------------------------------------------------------\n",
    "# Per-seed z estimates: fit z independently for each replicate trajectory.\n",
    "# This is the primary uncertainty estimate — it directly reflects run-to-run\n",
    "# variability in tau_int rather than relying on OLS residuals over 6 sizes.\n",
    "# ---------------------------------------------------------------------------\n",
    "def _per_seed_z(L: np.ndarray, samples: np.ndarray) -> np.ndarray:\n",
    "    \"\"\"Return z fitted independently for each seed column in samples (n_size, n_seed).\"\"\"\n",
    "    n_seeds = samples.shape[1]\n",
    "    z_arr = np.full(n_seeds, np.nan)\n",
    "    for s in range(n_seeds):\n",
    "        col = samples[:, s]\n",
    "        valid = np.isfinite(col) & (col > 0)\n",
    "        if valid.sum() >= 3:\n",
    "            z_arr[s] = fit_loglog(L[valid], col[valid])['z']\n",
    "    return z_arr[np.isfinite(z_arr)]\n",
    "\n",
    "\n",
    "z_seeds_m = _per_seed_z(L_metro, tau_metro_samples)\n",
    "z_seeds_w = _per_seed_z(L_wolff, tau_wolff_samples)\n",
    "\n",
    "z_m_med  = float(np.median(z_seeds_m))\n",
    "z_w_med  = float(np.median(z_seeds_w))\n",
    "z_m_p16, z_m_p84 = float(np.percentile(z_seeds_m, 16)), float(np.percentile(z_seeds_m, 84))\n",
    "z_w_p16, z_w_p84 = float(np.percentile(z_seeds_w, 16)), float(np.percentile(z_seeds_w, 84))\n",
    "\n",
    "# OLS fit on the per-size medians: used for the reference curve and CI band only.\n",
    "fit_m = fit_loglog(L_metro, tau_metro_med)\n",
    "fit_w = fit_loglog(L_wolff, tau_wolff_med)\n",
    "\n",
    "L_fit = np.linspace(min(np.min(L_metro), np.min(L_wolff)),\n",
    "                    max(np.max(L_metro), np.max(L_wolff)), 300)\n",
    "tau_fit_m, tau_fit_m_lo, tau_fit_m_hi = mean_band(fit_m, np.log(L_fit))\n",
    "tau_fit_w, tau_fit_w_lo, tau_fit_w_hi = mean_band(fit_w, np.log(L_fit))\n",
    "\n",
    "# ---------------------------------------------------------------------------\n",
    "# Figure: Left — scaling plot with seed uncertainty bands.\n",
    "#         Right — per-seed z distributions (the primary uncertainty view).\n",
    "# ---------------------------------------------------------------------------\n",
    "fig, axes = plt.subplots(1, 2, figsize=(13, 5))\n",
    "\n",
    "# --- Left panel: tau_int(L) scaling ---\n",
    "ax = axes[0]\n",
    "yerr_m = np.vstack([tau_metro_med - tau_metro_p16, tau_metro_p84 - tau_metro_med])\n",
    "yerr_w = np.vstack([tau_wolff_med - tau_wolff_p16, tau_wolff_p84 - tau_wolff_med])\n",
    "\n",
    "ax.errorbar(L_metro, tau_metro_med, yerr=yerr_m,\n",
    "            fmt='o', color=PALETTE['metro'], markersize=6, capsize=3,\n",
    "            label=f'Metropolis  $z = {z_m_med:.2f}$ [{z_m_p16:.2f}, {z_m_p84:.2f}]')\n",
    "ax.errorbar(L_wolff, tau_wolff_med, yerr=yerr_w,\n",
    "            fmt='s', color=PALETTE['wolff'], markersize=6, capsize=3,\n",
    "            label=f'Wolff (cs)  $z = {z_w_med:.2f}$ [{z_w_p16:.2f}, {z_w_p84:.2f}]')\n",
    "\n",
    "ax.loglog(L_fit, tau_fit_m, '--', color=PALETTE['metro'], alpha=0.9)\n",
    "ax.loglog(L_fit, tau_fit_w, '--', color=PALETTE['wolff'], alpha=0.9)\n",
    "ax.fill_between(L_fit, tau_fit_m_lo, tau_fit_m_hi, color=PALETTE['metro'], alpha=0.15)\n",
    "ax.fill_between(L_fit, tau_fit_w_lo, tau_fit_w_hi, color=PALETTE['wolff'], alpha=0.15)\n",
    "\n",
    "ax.set_xlabel('Lattice size $L$')\n",
    "ax.set_ylabel(r'Integrated autocorrelation time $\\tau_{\\mathrm{int}}$')\n",
    "ax.set_title(fr'Scaling at $T_c \\approx {Tc:.4f}$  (error bars: 16–84% over seeds)')\n",
    "ax.legend(fontsize=9, title='16–84% from per-seed z', title_fontsize=8)\n",
    "ax.grid(True, which='both', alpha=0.25)\n",
    "\n",
    "# --- Right panel: per-seed z distributions ---\n",
    "ax = axes[1]\n",
    "n_m = len(z_seeds_m)\n",
    "n_w = len(z_seeds_w)\n",
    "\n",
    "rng = np.random.default_rng(42)\n",
    "jitter_m = rng.uniform(-0.15, 0.15, n_m)\n",
    "jitter_w = rng.uniform(-0.15, 0.15, n_w)\n",
    "\n",
    "ax.scatter(np.ones(n_m) + jitter_m, z_seeds_m,\n",
    "           color=PALETTE['metro'], alpha=0.6, s=30, zorder=3)\n",
    "ax.scatter(2 * np.ones(n_w) + jitter_w, z_seeds_w,\n",
    "           color=PALETTE['wolff'], alpha=0.6, s=30, zorder=3)\n",
    "\n",
    "for x_pos, med, p16, p84, col in [\n",
    "    (1, z_m_med, z_m_p16, z_m_p84, PALETTE['metro']),\n",
    "    (2, z_w_med, z_w_p16, z_w_p84, PALETTE['wolff']),\n",
    "]:\n",
    "    ax.plot([x_pos - 0.25, x_pos + 0.25], [med, med], '-', color=col, lw=2.5, zorder=4)\n",
    "    ax.plot([x_pos, x_pos], [p16, p84], '-', color=col, lw=1.5, alpha=0.7, zorder=4)\n",
    "\n",
    "ax.set_xticks([1, 2])\n",
    "ax.set_xticklabels(['Metropolis', 'Wolff (cluster-step)'])\n",
    "ax.set_ylabel('Fitted dynamical exponent $z$')\n",
    "ax.set_title(f'Per-seed $z$ distribution  ({n_m} Metro, {n_w} Wolff seeds)')\n",
    "ax.grid(axis='y', alpha=0.25)\n",
    "ax.set_xlim(0.5, 2.5)\n",
    "\n",
    "fig.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# ---------------------------------------------------------------------------\n",
    "# Summary table\n",
    "# ---------------------------------------------------------------------------\n",
    "print('z from per-seed fit distribution (primary estimate):')\n",
    "print('-' * 70)\n",
    "print(f'  Metropolis     z = {z_m_med:.3f}  (16–84%: {z_m_p16:.3f} – {z_m_p84:.3f})  n_seeds = {n_m}')\n",
    "print(f'  Wolff (cs)     z = {z_w_med:.3f}  (16–84%: {z_w_p16:.3f} – {z_w_p84:.3f})  n_seeds = {n_w}')\n",
    "print()\n",
    "print('OLS fit on per-size medians (reference line on left panel):')\n",
    "print('-' * 70)\n",
    "print(f\"  Metropolis     z = {fit_m['z']:.3f}  (OLS SE: {fit_m['z_se']:.3f},  R² = {fit_m['r2']:.4f})\")\n",
    "print(f\"  Wolff (cs)     z = {fit_w['z']:.3f}  (OLS SE: {fit_w['z_se']:.3f},  R² = {fit_w['r2']:.4f})\")\n",
    "print()\n",
    "print('Note: Wolff z is in cluster-step units; sweep-equivalent z ≈ z_cs − 0.25.')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4dd89580",
   "metadata": {},
   "source": [
    "## Reading the result\n",
    "\n",
    "The core signal is the separation of slopes:\n",
    "- Metropolis remains near the textbook local-dynamics regime ($z \\approx 2.17$).\n",
    "- Wolff (in cluster-step units) yields a slope $z^{\\mathrm{cs}} \\approx 0.40$ at these system sizes ($L = 16$–$128$), approaching the asymptotic value $z^{\\mathrm{cs}} \\approx 0.5$ as $L \\to \\infty$. This indicates that cluster updates change the scaling law rather than only reducing a prefactor.\n",
    "\n",
    "**Unit interpretation.** The Wolff slope reported here is the cluster-step exponent $z^{\\mathrm{cs}}$. In sweep-equivalent units the normalised exponent is\n",
    "$$z^{\\mathrm{sw}} = z^{\\mathrm{cs}} - \\tfrac{1}{4} \\approx 0.25,$$\n",
    "which follows from $\\langle C \\rangle \\sim L^{\\gamma/\\nu} = L^{7/4}$ (exact 2D Ising FK scaling). This is roughly 9× smaller than the Metropolis exponent — a dramatic reduction, though not complete elimination of critical slowing down. For a full normalised comparison see the [Wolff Efficiency](wolff_efficiency.ipynb) notebook.\n",
    "\n",
    "Use the confidence intervals as stability diagnostics, not as strict final error bars, because finite-size windows and replicate counts in the cache can differ across runs. The right panel shows the per-seed $z$ distribution; a tight cluster near the median indicates a stable power-law regime over the measured $L$ range."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0aa4483",
   "metadata": {},
   "source": [
    "## Scientific implication\n",
    "\n",
    "For equilibrium sampling near criticality, Wolff is generally the right algorithmic choice because it suppresses critical slowing down while preserving the Boltzmann target distribution.\n",
    "\n",
    "However, a smaller algorithmic $z$ does **not** mean Wolff reproduces physical kinetic time. For non-equilibrium kinetics and dynamic universality studies tied to local physical updates, random-site Metropolis (or another local dynamics) remains the physically interpretable model, even when it is computationally slower."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bibliography-section",
   "metadata": {},
   "source": [
    "## Bibliography\n",
    "\n",
    "[[1]](#Bibliography) L. Onsager, \"Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition,\" *Physical Review*, vol. 65, no. 3-4, pp. 117-149, 1944. [APS Open Access](https://journals.aps.org/pr/abstract/10.1103/PhysRev.65.117)\n",
    "\n",
    "[[2]](#Bibliography) U. Wolff, \"Collective Monte Carlo Updating for Spin Systems,\" *Physical Review Letters*, vol. 62, no. 4, pp. 361-364, 1989. [APS Open Access](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.62.361)\n",
    "\n",
    "[[3]](#Bibliography) A. D. Sokal, \"Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms,\" lecture notes (1989), published in *Functional Integration: Basics and Applications* (C. DeWitt-Morette, P. Cartier, A. Folacci, eds.), Springer, 1997, pp. 131-192. Standard reference for integrated autocorrelation-time estimators and error analysis in Markov-chain Monte Carlo. [Springer Link](https://link.springer.com/chapter/10.1007/978-1-4899-0319-8_6)\n",
    "\n",
    "[[4]](#Bibliography) C. M. Fortuin and P. W. Kasteleyn, \"On the random-cluster model. I. Introduction and relation to other models,\" *Physica*, vol. 57, no. 4, pp. 536-564, 1972. Original paper introducing the random-cluster (FK) representation that underpins the Wolff and Swendsen–Wang algorithms. [Elsevier Open Access](https://doi.org/10.1016/0031-8914(72)90045-6)"
   ]
  }
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