Extending multiple histogram reweighting to a continuous lattice spin system exhibiting a first order phase transition

TL;DR

This paper extends the multiple histogram reweighting technique to a continuous lattice spin system with a first order phase transition, enabling efficient computation of various thermodynamic quantities.

Contribution

It introduces a novel approach that avoids constructing two-dimensional histograms, improving computational efficiency in analyzing phase transitions.

Findings

Accurate determination of transition temperature using finite size scaling.

Effective calculation of magnetization, susceptibility, and cumulants.

Enhanced computational efficiency in Monte Carlo simulations.

Abstract

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, 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.