Finite-temperature ordering in a two-dimensional highly frustrated spin model

TL;DR

This paper studies the finite-temperature phase transitions of a classical model derived from a highly frustrated kagome lattice, revealing a thermal order-by-disorder mechanism and small transition temperatures through Monte Carlo simulations.

Contribution

It introduces a classical model for a frustrated kagome lattice and demonstrates a thermal order-by-disorder transition with detailed Monte Carlo analysis.

Findings

Identification of a 120° spin structure in one case

Detection of a small finite transition temperature in the degenerate case

Evidence of thermal order-by-disorder mechanism

Abstract

We investigate the classical counterpart of an effective Hamiltonian for a strongly trimerized kagome lattice. Although the Hamiltonian only has a discrete symmetry, the classical groundstate manifold has a continuous global rotational symmetry. Two cases should be distinguished for the sign of the exchange constant. In one case, the groundstate has a 120^\circ spin structure. To determine the transition temperature, we perform Monte-Carlo simulations and measure specific heat, the order parameter as well as the associated Binder cumulant. In the other case, the classical groundstates are macroscopically degenerate. A thermal order-by-disorder mechanism is predicted to select another 120^\circ spin-structure. A finite but very small transition temperature is detected by Monte-Carlo simulations using the exchange method.