Multicanonical Simulations Step by Step

TL;DR

This paper provides a comprehensive guide and code for multicanonical simulations in statistical physics, demonstrating reproducible results for Potts and Ising models and introducing analysis techniques for large sums.

Contribution

It offers a starter kit with Fortran code and detailed simulation procedures for multicanonical sampling in various dimensions, including analysis methods for large data sums.

Findings

Reproducible simulation results for 2D Ising and 10-state Potts models.

Comparison of simulation data with exact results for thermodynamic quantities.

Introduction of an all-log jackknife technique for data analysis.

Abstract

The purpose of this article is to provide a starter kit for multicanonical simulations in statistical physics. Fortran code for the $q$-state Potts model in $d=2, 3,...$ dimensions can be downloaded from the Web and this paper describes simulation results, which are in all details reproducible by running prepared programs. To allow for comparison with exact results, the internal energy, the specific heat, the free energy and the entropy are calculated for the $d=2$ Ising ($q=2$) and the $q=10$ Potts model. % in a temperature range from $T=\infty$ down to sufficiently low % temperatures, such that the groundstates are included in the sampling. Analysis programs, relying on an all-log jackknife technique, which is suitable for handling sums of very large numbers, are introduced to calculate our final estimators.