References

• W. Krauth, Statistical Mechanics: Algorithms and Computations, Oxford University Press, 2006.

• N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, Equation of State Calculations by Fast Computing Machines, J. Chem. Phys. 21, 1087 (1953).

• Adrian Del Maestro, Introduction to classical Monte Carlo methods, github repository.

• P. Young, Everything You Wanted to Know About Data Analysis and Fitting but Were Afraid to Ask, arXiv:1210.3781 (2012).

• V. Ambegaokar and M. Troyer, Estimating errors reliably in Monte Carlo simulations of the Ehrenfest model, Am. J. of Phys. 78, 150 (2010).

Outline

• Introduction to Monte Carlo

• Newton–Cotes quadrature

• Importance sampling

• Direct sampling methods

• Markov chain sampling and balance condition

• Metropolis-Hastings algorithm

• The two-dimensional Ising model

• Error bar analysis

• References