Multicanonical Ensemble: A New Approach to Simulate First-order Phase Transitions

TL;DR

This paper introduces a multicanonical algorithm that efficiently simulates first-order phase transitions, significantly reducing tunneling times and enabling high-precision measurements in large lattice systems.

Contribution

The paper presents a novel multicanonical simulation method that overcomes exponential tunneling time growth in first-order phase transition studies.

Findings

Tunneling time scales as L^{2.65}, not exponentially.

Computational effort increases as V^{2.3} for large systems.

Achieved over two orders of magnitude improvement over standard algorithms.

Abstract

Relying on the recently proposed multicanonical algorithm, we present a numerical simulation of the first order phase transition in the 2d 10-state Potts model on lattices up to sizes $100\times100$. It is demonstrated that the new algorithm $lacks$ an exponentially fast increase of the tunneling time between metastable states as a function of the linear size $L$ of the system. Instead, the tunneling time diverges approximately proportional to $L^{2.65}$. Thus the computational effort as counted per degree of freedom for generating an independent configuration in the unstable region of the model rises proportional to $V^{2.3}$, where $V$ is the volume of the system. On our largest lattice we gain more than two orders of magnitude as compared to a standard heat bath algorithm. As a first physical application we report a high precision computation of the interfacial tension.