A comparison of two Monte Carlo Methods for computations in statistical mechanics
Abstract
A comparison of two Monte Carlo methods for computations in statistical mechanics is presented. In the comparison, involving a twostate problem, the transition probabilities introduced by Metropolis et al. are compared with the conditional probabilities of the Boltzmann distribution. The analytic relationship between the two is derived. Results of energy computations are given for an ising spin system on a triangular lattice using first one set of transition probabilities then the other. Both results are compared with the exact analytic solution. Greater stability and faster convergence was found when using the conditional Boltzmann probabilities. Also some results for the Monte Carlo method in general are presented.
 Publication:

Final Report National Bureau of Standards
 Pub Date:
 September 1974
 Bibcode:
 1974nbs..reptR....C
 Keywords:

 Monte Carlo Method;
 Statistical Mechanics;
 Boltzmann Transport Equation;
 Computation;
 Ferromagnetism;
 Markov Processes;
 Mathematical Models;
 Thermodynamics and Statistical Physics