Broad Histogram Method for Continuous Systems: the XY-Model

Abstract

We propose a way of implementing the Broad Histogram Monte Carlo method to systems with continuous degrees of freedom, and we apply these ideas to investigate the three-dimensional XY-model with periodic boundary conditions. We have found an excellent agreement between our method and traditional Metropolis results for the energy, the magnetization, the specific heat and the magnetic susceptibility on a very large temperature range. For the calculation of these quantities in the temperature range 0.7<T<4.7 our method took less CPU time than the Metropolis simulations for 16 temperature points in that temperature range. Furthermore, it calculates the whole temperature range 1.2<T<4.7 using only 2.2 times more computer effort than the Histogram Monte Carlo method for the range 2.1<T<2.2. Our way of treatment is general, it can also be applied to other systems with continuous degrees of freedom.

23 pages, 10 Postscript figures, to be published in Int. J. Mod. Phys. C

References in corpus (1)

• Broad Histogram Monte Carlo

Cited by in corpus (6)

• Transition Matrix Monte Carlo Method
• Generalized Ensemble Simulations for Complex Systems
• Speeding Up Computer Simulations: The Transition Observable Method
• Rejection-free Monte Carlo Algorithms for Models with Continuous Degrees of Freedom
• Broad Histogram Method for Multiparametric Hamiltonians
• The density of states of classical spin systems with continuous degrees of freedom