Thermodynamics of the classical spin-ice model with nearest neighbour interactions using the Wang-Landau algorithm

TL;DR

This study uses the Wang-Landau algorithm to explore the thermodynamics of the classical nearest-neighbour spin-ice model, revealing rich behaviors including residual entropy, kagome-ice phase, and Kasteleyn transition, serving as a benchmark for frustrated systems.

Contribution

It demonstrates the effectiveness of the Wang-Landau algorithm in analyzing complex magnetic frustration phenomena in spin-ice models, including phase transitions and entropy calculations.

Findings

Residual entropy of the nnSI model quantified.

Identification of kagome-ice phase under magnetic fields.

Observation of the three-dimensional Kasteleyn transition.

Abstract

In this article we study the classical nearest-neighbour spin-ice model (nnSI) by means of Monte Carlo simulations, using the Wang-Landau algorithm. The nnSI describes several of the salient features of the spin-ice materials. Despite its simplicity it exhibits a remarkably rich behaviour. The model has been studied using a variety of techniques, thus it serves as an ideal benchmark to test the capabilities of the Wang Landau algorithm in magnetically frustrated systems. We study in detail the residual entropy of the nnSI and, by introducing an applied magnetic field in two different crystallographic directions ([111] and [100],) we explore the physics of the kagome-ice phase, the transition to full polarisation, and the three dimensional Kasteleyn transition. In the latter case, we discuss how additional constraints can be added to the Hamiltonian, by taking into account a selective choice of states in the partition function and, then, show how this choice leads to the realization of the ideal Kasteleyn transition in the system.