Monte Carlo study on low-temperature phase diagrams of the $J_1$-$J_2$ classical $XY$ kagome antiferromagnet

Abstract

Frustrated magnets with degenerate ground states exhibit exotic ground states and rich phase structures when perturbations and/or thermal fluctuations lift the degeneracy. In two-dimensional models with short-range interactions, continuous symmetries cannot spontaneously break at finite temperatures, leading to the suppression of conventional magnetic long-range ordering (LRO). In this paper, we numerically study the classical $J_1$-$J_2$ $XY$ antiferromagnet on the kagome lattice as a prototype model of such frustrated magnets, where $J_2$ denotes the next-nearest-neighbor exchange interaction. We map out the $J_2$-$T$ phase diagram of this model employing extensive classical Monte Carlo (MC) simulations. The obtained phase diagram features Berezinskii-Kosterlitz-Thouless (BKT) transitions of $q=0$, $\sqrt{3}\times \sqrt{3}$ magnetic orders, and octupole orders, in addition to finite-temperature phase transitions of both ferrochiral and antiferrochiral long-range orders. Additionally, we find a non-trivial first-order transition for antiferromagnetic $J_2/J_1<0$. The origin of this transition is discussed in the context of non-local loop structures present in local $120^{\circ }$ spin structures.

References in corpus (3)

• Fictitious excitations in the classical Heisenberg antiferromagnet on the kagome lattice
• Tensor network approach to the fully frustrated XY model on a kagome lattice with a fractional vortex-antivortex pairing transition
• Nonequilibrium relaxation study of the anisotropic antiferromagnetic Heisenberg model on the triangular lattice

Cited by in corpus (2)

• Theory of charge-6e condensed phase in Kagome lattice superconductors
• Phase coherence of charge-$6e$ superconductors via a frustrated Kagome XY antiferromagnet