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

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.

arXiv comment9 pages, 9 figures

References in corpus (17)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Spin Ice State in Frustrated Magnetic Pyrochlore Materials
• Multicanonical Ensemble: A New Approach to Simulate First-order Phase Transitions
• Magnetic Monopoles in Spin Ice
• Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram
• Spin-lattice coupling in frustrated antiferromagnets
• Dipolar Interactions and Origin of Spin Ice in Ising Pyrochlore Magnets
• A New Approach to Spin Glass Simulations
• Fast Algorithm to Calculate Density of States
• Thermodynamic Properties of the Dipolar Spin Ice Model
• Theory of the [111] magnetization plateau in spin ice
• A Three Dimensional Kasteleyn Transition: Spin Ice in a [100] Field
• Magnetization process of spin ice in a [111] magnetic field
• Residual Entropy of Ordinary Ice from Multicanonical Simulations
• Corrections to Pauling residual entropy and single tetrahedron based approximations for the pyrochlore lattice Ising antiferromagnet
• First- order versus unconventional phase transitions in three-dimensional dimer models
• The Kasteleyn transition in three dimensions: spin ice in a [100] field

Cited by in corpus (10)

• Phase transitions, order by disorder and finite entropy in the Ising antiferromagnetic bilayer honeycomb lattice
• Entropy of the diluted antiferromagnetic Ising models on the frustrated lattices using the Wang-Landau method
• The 3D Kasteleyn transition in dipolar spin ice: a numerical study with the Conserved Monopoles Algorithm
• Large peaks in the entropy of the diluted nearest-neighbor spin-ice model on the pyrochlore lattice in a [111] magnetic field
• Proton strings and rings in atypical nucleation of ferroelectricity in ice
• Calculation of the Residual Entropy of Ice Ih by Monte Carlo simulation with the Combination of the Replica-Exchange Wang-Landau algorithm and Multicanonical Replica-Exchange Method
• Exact Results for the Residual Entropy of Ice Hexagonal Monolayer
• Residual Entropy of Ice: A Study Based on Transfer Matrices
• Equivalence of residual entropy of hexagonal and cubic ices from tensor network methods
• Phase Transition and Monopoles Densities in a Nearest Neighbors Two-Dimensional Spin Ice Model