Numerical transfer matrix study of frustrated next-nearest-neighbor Ising models on square lattices

TL;DR

This paper uses an advanced numerical transfer matrix method to study complex frustrated Ising models on square lattices, clarifying phase behaviors that are difficult to analyze with traditional approaches.

Contribution

It extends the transfer matrix approach to new frustrated Ising models, providing high-accuracy results that resolve previous ambiguities in phase formation.

Findings

Resolved ambiguities in phase formation of frustrated Ising models

Extended transfer matrix method to biaxial, diagonal, and third-nearest-neighbor frustrations

Provided comprehensive overview of modulated phases

Abstract

Ising models with frustrated next-nearest-neighbor interactions present a rich morphology of modulated phases. These phases, however, assemble and relax slowly, which hinders their computational study. In two dimensions, strong fluctuations further hamper determining their equilibrium phase behavior from theoretical approximations. The exact numerical transfer matrix (TM) method, which bypasses these difficulties, can serve as a benchmark method once its own numerical challenges are surmounted. Building on our recent study [Hu and Charbonneau, Phys. Rev. B 103, 094441 (2021)], in which we evaluated the two-dimensional axial next-nearest-neighbor Ising (ANNNI) model with transfer matrices, we here extend the effective usage of the TM method into the Ising models with biaxial, diagonal, and third-nearest-neighbor frustrations (BNNNI, DNNI, and 3NNI models). Thanks to the high-accuracy numerics provided by the TM results, various physical ambiguities about these reference models are resolved and an overview of modulated phase formation is obtained.