Entropy of diluted antiferromagnetic Ising models on 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 WangLandau 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. This paper is accepted for publication in Phys. Rev. E

Interplay of dilution and magnetic field in the nearest-neighbor spin-ice model on the pyrochlore lattice

“…Magnetic ions Dy or Ho are replaced by nonmagnetic Y ions. Nonmonotonic zeropoint entropy as a function of the dilute concentration was observed experimentally, and further studies on the dilution effects have been reported [14][15][16].…”

“…Magnetic ions Dy or Ho are replaced by nonmagnetic Y ions. Nonmonotonic zeropoint entropy as a function of the dilute concentration was observed experimentally, and further studies on the dilution effects have been reported [14][15][16].In this communication, we study the diluted nearestneighbor (NN) antiferromagnetic (AFM) Ising model on the pyrochlore lattice under a magnetic field in the [111] direction. We treat the NN interaction as a theoretical model; a more complicated model, such as the dipolar model, may be required to make connections to actual materials.…”

Large peaks in the entropy of the diluted nearest-neighbor spin-ice model on the pyrochlore lattice in a [111] magnetic field

“…In order to investigate the entropy, we use the Wang-Landau (WL) Monte Carlo method [18], which directly calculates the energy density of states (DOS), g(E). The precise estimates of the residual entropy for the diluted spin-ice model with no magnetic field were reported by Shevchenko et al [19]. If we use a canonical Monte Carlo simulation such as the Metropolis algorithm, the estimate arXiv:2108.04697v1 [cond-mat.dis-nn] 10 Aug 2021 of the entropy is obtained by the numerical integration of the specific heat.…”

Low-energy states, ground states, and variable frustrations of the finite-size dipolar Cairo lattices

“…It is impossible to realize antiferromagnetic order over the entire triangle-at least two spins are ordered ferromagnetically and at least one connection will be inevitably frustrated. Understanding the physics of frustrations is essential to understanding the properties of many materials such as spin and macrospin glasses [2,3], water ice [4,5], spin ice and artificial spin ice [6][7][8][9][10][11][12][13][14][15][16][17][18], and many others.…”