Monte Carlo

Any stochastic method for performing a multi-dimensional integral can be referred to as Monte Carlo (MC), although the term typically means a simulation technique that employs some version of the Metropolis algroithm to probe the thermodynamic properties of a system in equilibrium [1,2,3]. The traditional Metropolis algorithm is a Markov process in which trial moves are accepted or rejected in order to sample the Bolztmann distribution.

Figure 1: Traditional Metropolis moves can be very ineffective for a sufficiently low-temperature simulation with a complex potential energy surface. Configurations will not be able to escape energy barriers and will not explore configuration space efficiently.