Resolving the two-dimensional ANNNI model using transfer matrices

TL;DR

This paper introduces a transfer matrix method to accurately analyze the phase diagram of the two-dimensional ANNNI model, resolving previous ambiguities caused by long correlations and simulation difficulties.

Contribution

The authors develop a transfer matrix approach that overcomes longstanding challenges in studying the 2D ANNNI model's phase transitions and phase diagram.

Findings

Confirmed transition temperatures of the model

Clarified the order of the transition to the incommensurate phase

Provided a new framework for analyzing similar models

Abstract

The phase diagram of the two-dimensional ANNNI model has long been theoretically debated. Extremely long structural correlations and relaxation times further result in numerical simulations making contradictory predictions. Here, we introduce a numerical transfer matrix treatment that bypasses these problems, and thus overcome various ambiguities in the phase diagram. In particular, we confirm the transition temperatures and clarify the order of the transition to the floating incommensurate phase. Our approach motivates considering transfer matrices for resolving long-standing problems in related statistical physics models.