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.
Highlights
In magnetism, when a spin cannot fully minimise its interactions with its neighbours, the system is called “frustrated”
In this work we have explored by means of the Wang-Landau algorithm (WLA) the nearest-neighbour spin-ice model, an example of a simple classical frustrated model
We have determined the value of the residual entropy S0 by doing a finite size analysis of S0(L) which can be calculated directly from the density of states (DoS) determined by the WLA for samples of size L3
Summary
In magnetism, when a spin cannot fully minimise its interactions with its neighbours, the system is called “frustrated”. Frustrated systems exhibit a rich variety of behaviour, including order by disorder, fractionalisation and magnetic analogues of solids, liquids, glasses, ice, quantum liquids and Bose condensation. They represent ideal model systems for the study of generic concepts relevant to collective phenomena, where simple classical Hamiltonians can give rise to a wealth of different phenomena [1,2,3]. All this make geometrically frustrated systems the focus of attention of both theoretical and experimental research, making for ideal test-grounds for numerical techniques
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