Figure 8.14: Flow diagram for the DMC algorithm applied to melt simulation

9.1. Limitation of Metropolis Scheme:

.....We have so far discussed the MC simulations, which are based on the Metropolis scheme. In the Metropolis scheme, sampling of energy states is biased towards the more favorable energy states. It fails to sample those events (or states) for which the probability is very low.

.....Consider the following energy distribution of any system at a temperature, T (> 0K):

Figure 9.1: Schematic of energy distribution

Clearly, the sampling probability of E' and E” is extremely less. Hence, the system for which the low probable states are crucial cannot be simulated using the Metropolis Monte Carlo method.