Entropy of the diluted antiferromagnetic Ising models on the frustrated lattices using the Wang-Landau method

Abstract

We use a Monte Carlo simulation to study the diluted antiferromagnetic Ising model on the frustrated lattices including the pyrochlore lattice to show the dilution effects. Using the Wang-Landau algorithm, which directly calculates the energy density of states, we accurately calculate the entropy of the system. We discuss the nonmonotonic dilution concentration dependence of residual entropy for the antiferromagnetic Ising model on the pyrochlore lattice, and compare it to the generalized Pauling approximation proposed by Ke et al. [Phys. Rev. Lett. 99, 137203 (2007)]. We also investigate other frustrated systems, the antiferromagnetic Ising model on the triangular lattice and the kagome lattice, demonstrating the difference in the dilution effects between the system on the pyrochlore lattice and that on other frustrated lattices.

References in corpus (16)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Spin Ice State in Frustrated Magnetic Pyrochlore Materials
• Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram
• Fast Algorithm to Calculate Density of States
• Why spin ice obeys the ice rules
• A new macroscopically degenerate ground state in the spin ice compound Dy2Ti2O7 under a magnetic field
• A generic, hierarchical framework for massively parallel Wang-Landau sampling
• Non-monotonic zero point entropy in diluted spin ice
• Analysis of the convergence of the 1/t and Wang-Landau algorithms in the calculation of multidimensional integrals
• Effect of magnetoelastic coupling on spin-glass behavior in Heisenberg pyrochlore antiferromagnets with bond disorder
• Difference of energy density of states in the Wang-Landau algorithm
• Non-monotonic residual entropy in diluted spin ice: a comparison between Monte Carlo simulations of diluted dipolar spin ice models and experimental results
• Self-averaging of random and thermally disordered diluted Ising systems
• Suppression of Pauling's Residual Entropy in Dilute Spin Ice (Dy${}_{1-x}$Y${}_x$)${}_2$Ti${}_2$O${}_7$
• Thermodynamics of the classical spin-ice model with nearest neighbour interactions using the Wang-Landau algorithm
• Interplay of dilution and magnetic field in the nearest-neighbor spin-ice model on the pyrochlore lattice

Cited by in corpus (4)

• Large peaks in the entropy of the diluted nearest-neighbor spin-ice model on the pyrochlore lattice in a [111] magnetic field
• Comparison of diluted antiferromagnetic Ising models on frustrated lattices in a magnetic field
• Exact Results for the Residual Entropy of Ice Hexagonal Monolayer
• Residual Entropy of Ice: A Study Based on Transfer Matrices