Appendix D: Further Reading & References

D.1 Textbooks

Newman, M. E. J. & Barkema, G. T. — Monte Carlo Methods in Statistical Physics (Oxford, 1999). The standard graduate text. Covers Ising, Potts, cluster algorithms, and finite-size scaling in depth.
Frenkel, D. & Smit, B. — Understanding Molecular Simulation (Academic Press, 3rd ed. 2023). The reference for MC and MD in chemical physics. Comprehensive treatment of free energy methods.
Landau, D. P. & Binder, K. — A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge, 4th ed. 2014). Encyclopaedic coverage of algorithms and applications.
Krauth, W. — Statistical Mechanics: Algorithms and Computations (Oxford, 2006). Elegant and rigorous; excellent on cluster algorithms and MCMC theory.

Gelman, A. et al. — Bayesian Data Analysis (CRC Press, 3rd ed. 2013). Standard reference for Bayesian inference and MCMC.
Robert, C. P. & Casella, G. — Monte Carlo Statistical Methods (Springer, 2nd ed. 2004). Mathematically rigorous treatment of MCMC convergence.

Voter, A. F. — “Introduction to the Kinetic Monte Carlo Method”, in Radiation Effects in Solids (Springer, 2007). The clearest introductory review.
Reuter, K. — “First-Principles Kinetic Monte Carlo Simulations for Heterogeneous Catalysis”, in Modelling and Simulation of Heterogeneous Catalytic Reactions (Wiley-VCH, 2011).

Metropolis, N. et al. — “Equation of State Calculations by Fast Computing Machines”, J. Chem. Phys. 21, 1087 (1953). The original Metropolis paper.
Hastings, W. K. — “Monte Carlo Sampling Methods Using Markov Chains and Their Applications”, Biometrika 57, 97 (1970).
Swendsen, R. H. & Wang, J.-S. — “Nonuniversal Critical Dynamics in Monte Carlo Simulations”, Phys. Rev. Lett. 58, 86 (1987). Cluster algorithm.
Wolff, U. — “Collective Monte Carlo Updating for Spin Systems”, Phys. Rev. Lett. 62, 361 (1989).
Wang, F. & Landau, D. P. — “Efficient, Multiple-Range Random Walk Algorithm to Calculate the Density of States”, Phys. Rev. Lett. 86, 2050 (2001).
Geyer, C. J. — “Markov Chain Monte Carlo Maximum Likelihood”, Proc. 23rd Symp. Interface (1991). Parallel tempering.
Bortz, A. B., Kalos, M. H. & Lebowitz, J. L. — “A New Algorithm for Monte Carlo Simulation of Ising Spin Systems”, J. Comput. Phys. 17, 10 (1975). The BKL algorithm.
Gillespie, D. T. — “Exact Stochastic Simulation of Coupled Chemical Reactions”, J. Phys. Chem. 81, 2340 (1977).

Onsager, L. — “Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition”, Phys. Rev. 65, 117 (1944).
Kosterlitz, J. M. & Thouless, D. J. — “Ordering, Metastability and Phase Transitions in Two-Dimensional Systems”, J. Phys. C 6, 1181 (1973).
Mermin, N. D. & Wagner, H. — “Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models”, Phys. Rev. Lett. 17, 1133 (1966).

Kirkpatrick, S., Gelatt, C. D. & Vecchi, M. P. — “Optimization by Simulated Annealing”, Science 220, 671 (1983).
Reuter, K. & Scheffler, M. — “Composition, Structure, and Stability of RuO₂(110) as a Function of Oxygen Pressure”, Phys. Rev. B 65, 035406 (2001). First-principles KMC.
Castelnovo, C., Moessner, R. & Sondhi, S. L. — “Magnetic Monopoles in Spin Ice”, Nature 451, 42 (2008).

Binder, K. — “Monte Carlo Simulations in Statistical Physics”, Am. J. Phys. 80, 1099 (2012). Excellent overview for physicists.
Betancourt, M. — “A Conceptual Introduction to Hamiltonian Monte Carlo”, arXiv:1701.02434 (2017). Best pedagogical treatment of HMC.
Voter, A. F. — “Hyperdynamics: Accelerated Molecular Dynamics of Infrequent Events”, Phys. Rev. Lett. 78, 3908 (1997). Foundation of accelerated dynamics methods.
Rohwedder, T. & Schneider, R. — “Error Estimates for the Coupled Cluster Method”, ESAIM (2013). For context on quantum chemistry methods.

Package	Purpose	Language
LAMMPS	Molecular dynamics + MC	C++
GROMACS	MD with free energy	C++/CUDA
HOOMD-blue	GPU MC/MD	Python/C++
PyMC	Bayesian MCMC	Python
emcee	Affine-invariant MCMC	Python
MCNP6	Neutron/photon transport	Fortran
Geant4	Particle detector simulation	C++
SPPARKS	KMC for materials	C++
KMCLib	Lattice KMC	Python/C++
ASE	Atomic simulation environment	Python
vegas	Adaptive MC integration	Python
scipy.stats.qmc	Quasi-MC sequences	Python

Computational Physics course notes, Krauth (ENS Paris): https://www.lps.ens.fr/~krauth/
NIST Digital Library of Mathematical Functions: https://dlmf.nist.gov
TestU01 RNG testing library: https://simul.iro.umontreal.ca/testu01/
OpenKIM: verified interatomic potentials for KMC/MD: https://openkim.org
Materials Project: DFT-computed properties for KMC input: https://materialsproject.org