Classical Monte Carlo Method

In the context of condensed matter physics, methods of Markov-chain Monte Carlo simulation for many-body systems obeying classical statistical mechanics are called classical Monte Carlo methods. The representative example is the one by the Metropolis-Hastings method. The Markov-chain Monte Carlo method for simulated annealing is also a classical Monte Carlo method. In particular, a local update method is the method in which a degree of freedom is selected at each step for update. A local update generally suffers from the slow convergence near the critical point (critical slowing-down). To solve this problem, global update methods are proposed, in which a group of elements are updated at each time. However, it is necessary to design the algorithm depending on each specific system, and the applicability of the algorithm is limited compared to the local update methods.