First-Order Transition to Incommensurate Phase with Broken Lattice Rotation Symmetry in Frustrated Heisenberg Model

TL;DR

This study investigates a finite-temperature phase transition in a frustrated 2D Heisenberg model on a triangular lattice, revealing a first-order transition with broken lattice rotation symmetry at a specific interaction ratio.

Contribution

It demonstrates a first-order phase transition with lattice rotation symmetry breaking in a frustrated Heisenberg model, highlighting the role of third-nearest-neighbor interactions.

Findings

First-order phase transition observed at J_3/J_1 = -3.

Breaking of threefold lattice rotation symmetry.

Ground state degeneracy related to lattice rotations.

Abstract

We study a finite-temperature phase transition in the two-dimensional classical Heisenberg model on a triangular lattice with a ferromagnetic nearest-neighbor interaction $J_1$ and an antiferromagnetic third-nearest-neighbor interaction $J_3$ using a Monte Carlo method. Apart from a trivial degeneracy corresponding to O(3) spin rotations,the ground state for $J_3 \neq 0$ has a threefold degeneracy corresponding to 120 degree lattice rotations. We find that this model exhibits a first-order phase transition with the breaking of the threefold symmetry when the interaction ratio is $J_3/J_1=-3$.