Classical Ring-exchange Processes on the Triangular Lattice

TL;DR

This study investigates classical ring-exchange interactions on a triangular lattice using Monte Carlo simulations, revealing phase transitions and critical phases depending on the number of spin states.

Contribution

It introduces a classical Monte Carlo analysis of ring-exchange Hamiltonians on the triangular lattice, highlighting phase behavior for different Q-states.

Findings

Q=6 exhibits a first-order transition to stripe order.

Q>6 shows a critical phase between stripe and paramagnetic phases.

The model demonstrates rich phase behavior depending on the number of spin states.

Abstract

The effects of the ring-exchange Hamiltonian H_3 = J_3 sum_{<ijk>} (S_i * S_j) (S_i * S_k) on the triangular lattice are studied using classical Monte Carlo simulations. Each spin $S_i$ is treated as a classical XY spin taking on Q equally spaced angles (Q-states clock model). For Q=6, a first-order transition into a stripe-ordered phase preempts the macroscopic classical degeneracy. For Q > 6, a finite window of critical phase exists, intervening between the low-temperature stripe phase and the high-temperature paramagnetic phase.