# Project Bibliography: VibeSpin This file collects all scientific references used throughout the VibeSpin project. It is a core part of the documentation, alongside PHYSICS.md and SCRIPTS.md. References are sorted by topic for clarity and review. All references are open-access or from reputable sources, and links are checked for accessibility. ## Referencing Policy Referencing policy is defined in [AGENTS.md](./agents.md#7-scientific-referencing). Please consult that file for the official rules and enforcement details. ## 1. Physical Models ### Ising Model - 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) - [Ising model on Wikipedia](https://en.wikipedia.org/wiki/Ising_model) ### XY Model - J. M. Kosterlitz and D. J. Thouless, "Ordering, metastability and phase transitions in two-dimensional systems," Journal of Physics C: Solid State Physics, vol. 6, no. 7, pp. 1181–1203, 1973. [IOP Open Access](https://iopscience.iop.org/article/10.1088/0022-3719/6/7/010) - N. D. Mermin and H. Wagner, "Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models," Physical Review Letters, vol. 17, no. 22, pp. 1133–1136, 1966. [APS Open Access](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.17.1133) - J. Villain, "Theory of one- and two-dimensional magnets with an easy magnetization plane. II. The planar, classical, two-dimensional magnet," J. Phys. France 36, 581-590 (1975). [Open Access](https://doi.org/10.1051/jphys:01975003606058100) - [XY model on Wikipedia](https://en.wikipedia.org/wiki/XY_model) ### q-state Clock Model - J. Lapilli, P. Pfeifer, and C. Wexler, "Universality away from critical points in two-dimensional phase transitions," Physical Review Letters, vol. 96, no. 14, 140603, 2006. [APS Open Access](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.96.140603) - [Clock model (Vector Potts model) on Wikipedia](https://en.wikipedia.org/wiki/Potts_model#Vector_Potts_model) --- ## 2. Algorithms ### Metropolis-Hastings Algorithm - W. K. Hastings, "Monte Carlo sampling methods using Markov chains and their applications," Biometrika, vol. 57, no. 1, pp. 97–109, 1970. [Oxford Academic](https://academic.oup.com/biomet/article/57/1/97/252073) - [Metropolis–Hastings algorithm on Wikipedia](https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm) ### Wolff Cluster Algorithm - 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) - [Wolff algorithm on Wikipedia](https://en.wikipedia.org/wiki/Wolff_algorithm) ### Fortuin-Kasteleyn Representation - 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. [Elsevier Open Access](https://doi.org/10.1016/0031-8914(72)90045-6) - [Random cluster model (Fortuin–Kasteleyn representation) on Wikipedia](https://en.wikipedia.org/wiki/Random_cluster_model) --- ## 3. Thermodynamic and Topological Observables ### Thermodynamics - K. Huang, "Statistical Mechanics," 2nd Edition, Wiley, 1987. [Statistical Mechanics lecture notes, John Cardy, Oxford (Archive)](https://arxiv.org/pdf/0807.3472.pdf) - [Magnetization on Wikipedia](https://en.wikipedia.org/wiki/Magnetization) - [Magnetic susceptibility on Wikipedia](https://en.wikipedia.org/wiki/Magnetic_susceptibility) - [Heat capacity on Wikipedia](https://en.wikipedia.org/wiki/Heat_capacity) ### Spatial Diagnostics - N. Goldenfeld, "Lectures on Phase Transitions and the Renormalization Group," Addison-Wesley, 1992. [Internet Archive (Open Access)](https://archive.org/details/lecturesonphaset0000gold) - [Correlation function on Wikipedia](https://en.wikipedia.org/wiki/Correlation_function_(statistical_mechanics)) - [Structure factor on Wikipedia](https://en.wikipedia.org/wiki/Structure_factor) ### Topological Diagnostics and BKT Transition - J. M. Kosterlitz and D. J. Thouless, "Ordering, metastability and phase transitions in two-dimensional systems," Journal of Physics C: Solid State Physics, vol. 6, no. 7, pp. 1181–1203, 1973. [IOP Open Access](https://iopscience.iop.org/article/10.1088/0022-3719/6/7/010) - [BKT transition on Wikipedia](https://en.wikipedia.org/wiki/Berezinskii%E2%80%93Kosterlitz%E2%80%93Thouless_transition) - [Vortex on Wikipedia](https://en.wikipedia.org/wiki/Vortex) - [Superfluid stiffness (Helicity modulus) on Wikipedia](https://en.wikipedia.org/wiki/Superfluid_stiffness) --- ## 4. Monte Carlo Analysis and Autocorrelation - G. S. Madras and A. D. Sokal, "The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk," Journal of Statistical Physics, vol. 50, no. 1-2, pp. 109–186, 1988. [Springer Open Access](https://link.springer.com/article/10.1007/BF01022990) - 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. [Springer Link](https://link.springer.com/chapter/10.1007/978-1-4899-0319-8_6) - [Autocorrelation time on Wikipedia](https://en.wikipedia.org/wiki/Autocorrelation#Time_series) - [Critical slowing down on Wikipedia](https://en.wikipedia.org/wiki/Critical_slowing_down) --- ## 5. Numerical and Computational Methods - Numba JIT and parallelization: [Numba documentation](https://numba.readthedocs.io/en/stable/user/parallel.html) --- ## 6. Additional References - M. E. J. Newman and G. T. Barkema, "Monte Carlo Methods in Statistical Physics," Oxford University Press, 1999. [Lecture Notes Summary (H. G. Katzgraber)](https://arxiv.org/abs/0905.1629) --- *This bibliography is maintained as a core project file. All references must be added here when cited elsewhere, and links must be checked for accessibility.*