Abstract—Phase transitions and critical phenomena are the most universal phenomena in nature. To understand the phase transitions and critical phenomena of a given system as a continuous function of temperature and to obtain the partition function zeros in the complex temperature plane indicating most effectively phase transitions and critical phenomena, we need to calculate the density of states. Currently, Wang-Landau Monte Carlo algorithm is one of the most efficient Monte Carlo methods to calculate the approximate density of states. Using Wang-Landau Monte Carlo algorithm, the density of states for the Ising model on L x L square lattices (L = 4 ~ 32) with periodic boundary conditions is obtained, and the partition function zeros of the Ising model are evaluated in the complex temperature plane. By examining the behavior of the first partition function zero (partition function zero closest to the positive real axis), phase transitions and critical phenomena can be much more accurately analyzed. The approximate first zeros of the Ising ferromagnet, obtained from Wang-Landau algorithm, are quite close to the exact ones, indicating that it is a reliable method for calculating the density of states and the first partition function zeros.
Index Terms—Phase transition, density of states, Ising model, partition function zeros.
Seung-Yeon Kim is with the School of Liberal Arts and Sciences, Korea National University of Transportation, Chungju 380-702, South Korea (e-mail: sykimm@ut.ac.kr).
Cite: Seung-Yeon Kim, "Evaluation of an Efficient Monte Carlo Algorithm to Calculate the Density of States," International Journal of Machine Learning and Computing vol. 2, no. 2, pp. 144-149 , 2012.