New multiple histogram method for studying phase transitions

Ralf K. Heilmann, A. M. Ferrenberg, D. P. Landau +1 more

Chin‐Kun Hu

J. Michael Kosterlitz, J. Lee, Enzo Granato

Suman Sinha

We present extensive Monte Carlo simulations on a two-dimensional XY model with a modified form of interaction potential. Thermodynamic quantities other than energy, specific heat, etc. (such as magnetization, susceptibility, and fourth-order cumulant of magnetization) are obtained using multiple histogram reweighting of the data obtained from the simulations. We employ an approach which eliminates the need to construct two-dimensional histograms. This approach makes judicious use of computer memory as well as CPU time. Lee-Kosterlitz's method of finite size scaling for a first-order transition and analysis using Binder's cumulant method allow us to make an accurate determination of the transition temperature.

Petras J. Kundrotas, Saulius Lapinskas, Anders Rosengren

The three-state antiferromagnetic Potts model on the simple cubic lattice is studied by the Monte Carlo method using a new order parameter and employing the histogram technique. It is shown that apart from the low-temperature broken-sublattice-symmetry phase with nonequivalent sublattices, another type of ordering with equivalent sublattices does exist in the model between the broken-sublattice-symmetry and disordered phases. The temperature of the transition between the ordered phases is estimated from the histogram of the order parameter. The value obtained is in good agreement with that obtained from cluster variation circulations.

Walter Greiner, Ludwig Neise, Horst Stöcker B