A generalized Monte Carlo loop algorithm for frustrated Ising models

TL;DR

This paper presents a Generalized Loop Move (GLM) algorithm that improves Monte Carlo sampling efficiency in frustrated Ising models with highly degenerate low-energy states, facilitating better exploration of complex energy landscapes.

Contribution

The paper introduces the GLM update, a novel Monte Carlo method tailored for frustrated Ising models, enhancing sampling in systems with extensive degenerate states.

Findings

GLM improves sampling efficiency in frustrated Ising models.

Effective in systems with degenerate and near-degenerate low-energy states.

Easily extendable to various lattice types and interactions.

Abstract

We introduce a Generalized Loop Move (GLM) update for Monte Carlo simulations of frustrated Ising models on two-dimensional lattices with bond-sharing plaquettes. The GLM updates are designed to enhance Monte Carlo sampling efficiency when the system's low-energy states consist of an extensive number of degenerate or near-degenerate spin configurations, separated by large energy barriers to single spin flips. Through implementation on several frustrated Ising models, we demonstrate the effectiveness of the GLM updates in cases where both degenerate and near-degenerate sets of configurations are favored at low temperatures. The GLM update's potential to be straightforwardly extended to different lattices and spin interactions allow it to be readily adopted on many other frustrated Ising models of physical relevance.