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 reexamines the classical J1-J2-J3 Ising model on the honeycomb lattice using Wang-Landau sampling and parallel tempering to map zero- and finite-temperature phase diagrams. It reveals a 20-fold ground-state degeneracy arising from four armchair and sixteen spiral configurations, and identifies the AC+SP coexistence with analytical ground-state boundaries. Finite-temperature analysis shows a spectrum of transitions from continuous to first-order, including a tricritical-like region near J3/J1=1.2 and a multipeak specific-heat phenomenon in strongly frustrated regimes, supported by energy histograms and finite-size scaling. The results refine the understanding of frustrated Ising systems and provide guidance for experimental searches of spiral states and specific-heat anomalies.

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.

Figures (12)

• Figure 1: The lattice structure of a honeycomb lattice is shown in (a) for the hexagonal representation and in (b) for the square-like arrangement, with $J_1$, $J_2$, and $J_3$ representing the nearest-neighbor, second-nearest neighbor, and third-nearest neighbor interactions, respectively.
• Figure 2: Phase diagram at zero temperature, which contains the ST, FM, and AC+SP phases. Different from Ref. th1, we find the AC phase should be coexist with the SP phase.
• Figure 3: Ground state spin configurations obtained from WL sampling. (a1)-(a4) show configurations of the AC phase, while (b1)-(b16) correspond to various spiral configurations. These 20 configurations are degenerate, which has not been found in previous works wildes2020th1zigzag. Red lines and arrows in (b1) indicate the spiral direction of spin configurations.
• Figure 4: Ground-state spin configurations for (a1)-(a2) the FM phase and (b1)-(b6) the ST phase.
• Figure 5: Structure factors corresponding to different configurations: (a1) for the AC phase; (a2) and (a3) is for the SP configurations; (b1)-(b3) for the ST configurations.