Spiral states, first-order transitions and specific heat multipeak phenomenon in $J_1$-$J_2$-$J_3$ Ising model: A Wang-Landau algorithm study

TL;DR

This study uses the Wang-Landau algorithm to analyze the $J_1$-$J_2$-$J_3$ Ising model on a honeycomb lattice, revealing complex phase coexistence, various phase transitions, and multipeak specific heat phenomena relevant to frustrated magnetic materials.

Contribution

It provides a detailed numerical investigation of the phase diagram and transition types in the $J_1$-$J_2$-$J_3$ Ising model, clarifying the nature of phases and transitions beyond previous mean-field studies.

Findings

Coexistence of armchair and spiral phases with 20-fold degeneracy.

Observation of first-order and continuous phase transitions.

Identification of multipeak specific heat phenomena in frustrated systems.

Abstract

The classical $J_1$-$J_2$-$J_3$ Ising model on the honeycomb lattice is important for understanding frustrated magnetic phenomena in materials such as FePS$_3$ and Ba$_2$CoTeO$_6$, where diverse phases (e.g., striped, zigzag, armchair) and magnetization plateaus have been experimentally observed. To explain the experimental results, previous mean-field studies have explored its thermal phase transitions, identifying armchair phases and striped phases, but their limitations call for more reliable numerical investigations. In this work, we systematically revisit the classical $J_1$-$J_2$-$J_3$ Ising model using the Wang-Landau algorithm. We find that the armchair (AC) phase, previously reported in mean-field and experimental studies, actually coexists with the spiral (SP) phase, with their combined degeneracy reaching 20-fold (4-fold for the AC states and 16-fold for the spiral states). The phase transitions and critical exponents are studied at different interaction values. We observe first-order phase transitions, continuous phase transitions, and even the multipeak phenomenon in frustrated systems. These results clarify the nature of phases and phase transitions in frustrated Ising systems and their exponents, and additionally provide inspiration for experimental efforts to search for the spiral state and specific-heat multipeak phenomenon.