Competing ferromagnetic and antiferromagnetic phases on the frustrated Ising honeycomb lattice

Pietro F. Dias; Fabio M. Zimmer; Nikolaos G. Fytas; Mateus Schmidt

paper

Competing ferromagnetic and antiferromagnetic phases on the frustrated Ising honeycomb lattice

arXiv:2601.19648

Abstract

We investigate the frustrated $J_{1}$ - $J_{2}$ - $J_{3}$ Ising model on the honeycomb lattice, featuring first- and second-neighbor ferromagnetic couplings ( $J_{1} > 0$ and $J_{2} > 0$ ) and third-neighbor antiferromagnetic interactions ( $J_{3} < 0$ ). Using the cluster mean-field method, we analyze the phase transitions in the regime $1/2 < J_{2} / J_{1} \leq 1$ , where ferromagnetic and antiferromagnetic phases compete. Our results reveal that near the strongly frustrated limit $J_{3} / J_{1} = - 1$ , the system exhibits order-by-disorder state selection, tricritical and bicritical behavior, critical endpoints, and two successive phase transitions. The ferromagnetic-paramagnetic transition remains second order across the entire interaction range, whereas the antiferromagnetic-paramagnetic boundary shows a richer behavior, including both first- and second-order transitions as well as tricriticality. Increasing the second-neighbor coupling $J_{2} / J_{1}$ narrows the range of $J_{3} / J_{1}$ where first-order antiferromagnetic-paramagnetic transitions occur; beyond a certain threshold, only second-order order-disorder transitions persist. Consequently, the tricritical point shifts toward $J_{3} / J_{1} \approx - 1$ as $J_{2} / J_{1}$ increases, culminating in a bicritical point where the antiferromagnetic, ferromagnetic, and paramagnetic phases meet.

Accepted for publication in Physica A