Entropic selection of magnetization in a frustrated 2D magnetic model

TL;DR

This paper investigates a frustrated 2D classical Heisenberg model with hexagonal spin clusters, revealing a degenerate ground state manifold with entropy-driven magnetization selection at finite temperatures.

Contribution

It provides an exact analysis of ground states in a frustrated 2D spin model and demonstrates entropy-driven magnetization selection through Monte Carlo simulations.

Findings

Ground state degeneracy exceeds global rotation symmetry

Finite temperature entropy influences magnetization values

Monte Carlo simulations reveal non-trivial magnetization histograms

Abstract

We discuss the magnetic ground state and properties of a frustrated two-dimensional classical Heisenberg model of interacting hexagonal clusters of spins. The energy of the ground states is found exactly for arbitrary values of $J_1$ (intra-cluster couplings) and $J_2$ (inter-cluster couplings). Our main results concern a frustrated region of the phase diagram, where we show that the set of ground states has a degeneracy larger than that due to global rotation symmetry. Furthermore, the ground state manifold does not have a fixed total magnetization~: there is a range of allowed values. At finite temperature, our Monte-Carlo simulations show that the entropy selects the most probable value of the total magnetization, while the histogram of the Monte-Carlo time series is non-trivial. This model is a first step towards modelling properties of a class of frustrated magnetic structures composed of coupled spin clusters.