Multicanonical Multigrid Monte Carlo

TL;DR

This paper introduces a combined multicanonical and multigrid Monte Carlo method to enhance simulation efficiency for first-order phase transitions, demonstrating significant improvements in two different physical models.

Contribution

The paper presents a novel integration of multicanonical and multigrid techniques for Monte Carlo simulations, achieving substantial performance gains.

Findings

Improvement factors of several times in quantum tunneling simulations.

Approximately tenfold efficiency increase in phase transition simulations.

Effective combination of methods for different dimensional models.

Abstract

To further improve the performance of Monte Carlo simulations of first-order phase transitions we propose to combine the multicanonical approach with multigrid techniques. We report tests of this proposition for the $d$-dimensional $\Phi^4$ field theory in two different situations. First, we study quantum tunneling for $d = 1$ in the continuum limit, and second, we investigate first-order phase transitions for $d = 2$ in the infinite volume limit. Compared with standard multicanonical simulations we obtain improvement factors of several resp. of about one order of magnitude.