The present investigation assessed the influence of quenched non-magnetic impurities over XY model in Kagome lattice. This study was performed using the Monte Carlos method and finite size scale theory in order to estimate BKT transition points with accuracy. The phase transition diagram obtained exhibits a region of topological order and a disordered region separated by a BKT transition line. The initial slope of the temperature with dilution outperformed value found for the square lattice.
The present investigation assessed the influence of quenched non-magnetic impurities over XY model in Kagome lattice. This study was performed using the Monte Carlos method and finite size scale theory in order to estimate BKT transition points with accuracy. The phase transition diagram obtained exhibits a region of topological order and a disordered region separated by a BKT transition line. The initial slope of the temperature with dilution outperformed value found for the square lattice.
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 Berezinskii-Kosterlitz-Thouless (BKT) transition in two-dimensional planar rotator and XY models on a square lattice, diluted by randomly placed vacancies, is studied here using hybrid Monte Carlo simulations that combine single spin flip, cluster and over-relaxation techniques. The transition temperature Tc is determined as a function of vacancy density ρvac by calculations of the helicity modulus and the by finite-size scaling of the in-plane magnetic susceptibility. The results for Tc are consistent with those from the much less precise fourth-order cumulant of Binder. Tc is found to decrease monotonically with increasing ρvac, and falls to zero close to the square lattice percolation limit, ρvac≈0.41 . The result is physically reasonable: the long-range orientational order of the low-temperature phase cannot be maintained in the absence of sufficient spin interactions across the lattice.
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 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 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.