Avoiding critical slowdown in models with SALR interactions

TL;DR

This paper investigates the critical slowdown in frustrated models with SALR interactions, providing insights from simplified models and proposing cluster algorithms that significantly accelerate simulations of the 2D ANNNI model.

Contribution

It offers a deeper understanding of critical slowdown in frustrated systems and introduces two cluster algorithms that enhance simulation speed for the 2D ANNNI model.

Findings

Achieved up to 40-fold speed-up in simulations.

Provided insights into the physics of critical slowdown.

Developed algorithms applicable to frustrated lattice models.

Abstract

In systems with frustration, the critical slowdown of the dynamics severely impedes the numerical study of phase transitions for even the simplest of lattice models. In order to help sidestep the gelation-like sluggishness, a clearer understanding of the underlying physics is needed. Here, we first obtain generic insights into that phenomenon by studying one-dimensional and Bethe lattice versions of a schematic frustrated model, the axial next-nearest neighbor Ising (ANNNI) model. Based on these findings, we formulate two cluster algorithms that speed up the simulations of the ANNNI model on a 2D square lattice. Although these schemes do not avoid the critical slowdown, speed-ups of factors up to 40 are achieved in some regimes.