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arXiv:2309.09659 · International Journal of Modern Physics C

Phase transitions in the anisotropic XY ferromagnet with quenched nonmagnetic impurity

Olivia Mallick, Muktish Acharyya

Published Dec 17, 2023• 2 citations
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Abstract

The equilibrium behaviors of the anisotropic XY ferromagnet, with nonmagnetic impurity, have been investigated in three dimensions by Monte Carlo simulation using Metropolis algorithm. Two different types of anisotropy, namely, the bilinear exchange type and single-site anisotropy are considered here. The thermodynamic behaviors of the components of the magnetizations (M), susceptibility ([Formula: see text]) and the specific heat (C) have been studied systematically through extensive Monte Carlo simulations. The ferro–para phase transition has been observed to take place at a lower temperature for impure anisotropic XY ferromagnet. The pseudocritical temperature ([Formula: see text]) has been found to decrease as the system gets more and more impure (impurity concentration p increases). In the case of bilinear exchange type of anisotropy ([Formula: see text]), the pseudocritical temperature ([Formula: see text]) increases linearly with [Formula: see text] for any given concentration of nonmagnetic impurity (p). The slope of this linear function has been found to depend on the impurity concentration (p). The slope decreases linearly with the impurity concentration (p). In the case of the single-site anisotropy (D), the pseudocritical temperature ([Formula: see text]) has been found to decrease linearly with p for fixed D. The critical temperature (for a fixed set of parameter values) has been estimated from the temperature variation of fourth-order Binder cumulants ([Formula: see text]) for different system sizes (L). The critical magnetization ([Formula: see text]) and the maximum value of the susceptibility ([Formula: see text]) are calculated for different system sizes (L). The critical exponents for the assumed scaling laws, [Formula: see text] and [Formula: see text], are estimated through the finite size analysis. We have estimated, [Formula: see text], equals [Formula: see text] and [Formula: see text] for bilinear exchange and single-site anisotropy, respectively. We have also estimated, [Formula: see text] equals [Formula: see text] and [Formula: see text] for bilinear exchange and single-site anisotropy, respectively.

DOI
10.1142/s0129183124500979

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The equilibrium behaviors of the anisotropic XY ferromagnet, with nonmagnetic impurity, have been investigated in three dimensions by Monte Carlo simulation using Metropolis algorithm. Two different types of anisotropy, namely, the bilinear exchange type and single-site anisotropy are considered here. The thermodynamic behaviors of the components of the magnetizations (M), susceptibility ([Formula: see text]) and the specific heat (C) have been studied systematically through extensive Monte Carlo simulations. The ferro–para phase transition has been observed to take place at a lower temperature for impure anisotropic XY ferromagnet. The pseudocritical temperature ([Formula: see text]) has been found to decrease as the system gets more and more impure (impurity concentration p increases). In the case of bilinear exchange type of anisotropy ([Formula: see text]), the pseudocritical temperature ([Formula: see text]) increases linearly with [Formula: see text] for any given concentration of nonmagnetic impurity (p). The slope of this linear function has been found to depend on the impurity concentration (p). The slope decreases linearly with the impurity concentration (p). In the case of the single-site anisotropy (D), the pseudocritical temperature ([Formula: see text]) has been found to decrease linearly with p for fixed D. The critical temperature (for a fixed set of parameter values) has been estimated from the temperature variation of fourth-order Binder cumulants ([Formula: see text]) for different system sizes (L). The critical magnetization ([Formula: see text]) and the maximum value of the susceptibility ([Formula: see text]) are calculated for different system sizes (L). The critical exponents for the assumed scaling laws, [Formula: see text] and [Formula: see text], are estimated through the finite size analysis. We have estimated, [Formula: see text], equals [Formula: see text] and [Formula: see text] for bilinear exchange and single-site anisotropy, respectively. We have also estimated, [Formula: see text] equals [Formula: see text] and [Formula: see text] for bilinear exchange and single-site anisotropy, respectively.
The three-dimensional anisotropic classical XY ferromagnet has been investigated by extensive Monte Carlo simulation using the Metropolis single spin flip algorithm. The magnetisation (M) and the susceptibility (χ) are measured and studied as functions of the temperature of the system. For constant anisotropy, the ferro-para phase transition has been found to take place at a higher temperature than that observed in the isotropic case. The system gets ordered at higher temperatures for higher values of the strength of anisotropy. The opposite scenario is observed in the case of random anisotropy. For all three different kinds of statistical distributions (uniform, Gaussian, and bimodal) of random anisotropy, the system gets ordered at lower temperatures for higher values of the width of the distribution of anisotropy. We have provided the phase boundaries in the case of random anisotropy. The critical exponents for the scaling laws M∼L−βν and χ∼Lγν are estimated through the finite size analysis.
The influence of quenched nonmagnetic impurities on phase transitions and critical phenomena in the 3D Potts model with the spin state number q = 4 is studied using the Monte Carlo method. Systems with the linear size L = 20–32 and spin concentrations p = 1.00, 0.90, 0.65 are considered. The fourth order Binder cumulant method is used to demonstrate that in the strongly diluted regime, a phase transition of the second kind is observed in this model for the spin concentration p = 0.65, and a phase transition of the first kind is observed for the pure ( p = 1.00) and weakly diluted ( p = 0.90) models. The theory of finite-dimensional scaling is used to calculate the static critical parameters of heat capacity α, susceptibility γ, magnetization β, and correlation radius ν.
Monte Carlo simulations are performed to analyze phase transitions in three-dimensional systems described by the 3-state Potts model with nonmagnetic impurities. Numerical results are presented for systems with spin concentrations p = 1.00, 0.95, 0.90, 0.80, 0.70, and 0.65 on lattices of size L varying between 20 and 44. Binder’s cumulant analysis shows that the introduction of quenched disorder in the form of non-magnetic impurities induces a crossover from first-order to second-order phase transition. The finite-size scaling method is used to calculate the static critical exponents α, γ, β, and ν for specific heat, susceptibility, magnetization, and correlation length, respectively.
The critical behavior of the disordered ferromagnetic Ising model is studied numerically by the Monte Carlo method in a wide range of variation of concentration of nonmagnetic impurity atoms. The temperature dependences of correlation length and magnetic susceptibility are determined for samples with various spin concentrations and various linear sizes. The finite-size scaling technique is used for obtaining scaling functions for these quantities, which exhibit a universal behavior in the critical region; the critical temperatures and static critical exponents are also determined using scaling corrections. On the basis of variation of the scaling functions and values of critical exponents upon a change in the concentration, the conclusion is drawn concerning the existence of two universal classes of the critical behavior of the diluted Ising model with different characteristics for weakly and strongly disordered systems.
The influence of quenched nonmagnetic impurities on phase transitions in the three-dimensional Potts model with the number of spin states q = 3 is investigated using the Wolff single-cluster algorithm of the Monte Carlo method. The systems with linear sizes L = 20–44 at the spin concentrations p = 1.0, 0.9, 0.8, and 0.7 are analyzed. It is demonstrated with the use of the method of fourth-order Binder cumulants that the second-order phase transition occurs in the model under consideration at the spin concentrations p = 0.9, 0.8, and 0.7 and that the first-order phase transition is observed in the pure model ( p = 1.0). The static critical exponents α (heat capacity), γ (susceptibility), β (magnetization), and ν (correlation length) are calculated in the framework of the finite-size scaling theory. The problem regarding the universality classes of the critical behavior of weakly diluted systems is discussed.
The effect of quenched nonmagnetic impurities on phase transitions in the three-dimensional Potts model with the number of spin states q=3 is studied using the Wolff single-cluster algorithm of the Monte Carlo method. By the method of fourth-order Binder cumulants, it is demonstrated that the second-order phase transition occurs in the model under study at spin concentrations p=0.9, 0.8, 0.7, and 0.65, while the first-order phase transition is observed in the pure model (p=1.0). The static critical exponents (CEs) α (heat capacity), γ (susceptibility), β (magnetization), and ν (correlation length) are calculated based on the finite-size scaling theory.