Condensed Matter Physics

DEPENDENCE OF THE CRITICAL TEMPERATURE ON MICROSCOPIC PARAMETERS IN THE THREE-DIMENSIONAL ISING-LIKE SYSTEMS

Mykhailo P. Kozlovskii, Dukhovii, Ihor V. Pylyuk

Published Jan 1, 2000• 3 citations

Abstract

The critical behaviour of the three-dimensional Ising-like system on a simple cubic lattice with an exponentially decreasing interaction potential is investigated within the collective variables method.The solution of the equation for the phase transition temperature is obtained by taking into account the dependence of its coefficients on the temperature.The dependence of the critical temperature on the interaction potential range is studied.

DOI: 10.5488/cmp.3.4.727

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Condensed Matter Physics

DEPENDENCE OF THE CRITICAL TEMPERATURE ON MICROSCOPIC PARAMETERS IN THE THREE-DIMENSIONAL ISING-LIKE SYSTEMS

Mykhailo P. Kozlovskii, Dukhovii, Ihor V. Pylyuk

Published Jan 1, 2000• 3 citations

Publisher

Abstract

DOI: 10.5488/cmp.3.4.727

Related papers

Study of the critical behaviour of three-dimensional Ising-like systems on the basis of the 6model with allowance for microscopic parameters: I. High-temperature region

I. R. Yukhnovskii, Ihor V. Pylyuk, Mykhailo P. Kozlovskii

The behaviour of a three-dimensional Ising-like system at temperatures above the critical value of T c is studied in the approximation of the sextic distribution for modes of spin density oscillations (ρ 6 model). The original collective variables method is developed in this higher non-Gaussian approximation for calculating the thermodynamic characteristics of the system near T c taking into account the first confluent correction. The calculations are illustrated by an example of a simple cubic lattice and an exponentially decreasing interaction potential. The main distinctive feature of the method is the separate inclusion of the contributions to the thermodynamic functions from the short-wave and long-wave spin density oscillation modes. The dependences of the phase transition temperature, leading critical amplitudes, and correction-to-scaling amplitudes for the specific heat and susceptibility on the microscopic parameters of the system are investigated.The behaviour of a three-dimensional Ising-like system at temperatures above the critical value of T c is studied in the approximation of the sextic distribution for modes of spin density oscillations (ρ 6 model). The original collective variables method is developed in this higher non-Gaussian approximation for calculating the thermodynamic characteristics of the system near T c taking into account the first confluent correction. The calculations are illustrated by an example of a simple cubic lattice and an exponentially decreasing interaction potential. The main distinctive feature of the method is the separate inclusion of the contributions to the thermodynamic functions from the short-wave and long-wave spin density oscillation modes. The dependences of the phase transition temperature, leading critical amplitudes, and correction-to-scaling amplitudes for the specific heat and susceptibility on the microscopic parameters of the system are investigated.

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physica status solidi (b)Oct 1, 199612 citations

Three-dimensional Ising models -- Critical Parameters using $ε$ -convergence method

M V Vismaya, M.V. Sangaranarayanan

We demonstrate the applicability of the $ε$ -convergence algorithm in extracting the critical temperatures and critical exponents of three-dimensional Ising models. We analyze the low temperature magnetization as well as high temperature susceptibility series of simple cubic, body-centered cubic, face-centered cubic and diamond lattices, using two different variables for the inverse critical temperature. In the case of simple cubic lattices, the magnetization series was modified to deduce accurate values of the critical temperatures. The alternate variable for dimensionless inverse temperature suggested by Guttmann and Thompson has also been employed for the estimation of the critical parameters.We demonstrate the applicability of the $ε$-convergence algorithm in extracting the critical temperatures and critical exponents of three-dimensional Ising models. We analyze the low temperature magnetization as well as high temperature susceptibility series of simple cubic, body-centered cubic, face-centered cubic and diamond lattices, using two different variables for the inverse critical temperature. In the case of simple cubic lattices, the magnetization series was modified to deduce accurate values of the critical temperatures. The alternate variable for dimensionless inverse temperature suggested by Guttmann and Thompson has also been employed for the estimation of the critical parameters.

arXiv:2410.15785Oct 21, 20240 citations

{T}_{c}

and are illustrated by an example of a simple cubic lattice and an exponentially decreasing interaction potential. The collective variables method makes it possible to obtain universal and nonuniversal quantities by using a unified approach. The dependence of the critical region size and phase-transition temperature on the microscopic parameters is investigated. A microscopic analog of the Landau free energy is calculated. Explicit expressions for the thermodynamic characteristics are obtained as functions of temperature and microscopic parameters of the system. It is shown that each of the leading critical amplitudes and correction-to-scaling amplitudes can be represented as a product of a universal factor not depending on the microscopic parameters of the system and a nonuniversal factor depending on these parameters. The thermodynamic characteristics near

{T}_{c}

and their amplitudes are given for various values of the effective radius of the exponentially decreasing interaction potential (including the values corresponding to the nearest-neighbor interaction and the interactions between the nearest and next-nearest neighbors and between the nearest, next-nearest, and third neighbors). The results of calculations and their comparison with other authors' data show that the ${\ensuremath{\rho}}^{6}$ model provides a better quantitative description of the critical behavior of a three-dimensional Ising ferromagnet than the ${\ensuremath{\rho}}^{4}$ model.

We demonstrate the applicability of the

ε

-convergence algorithm in extracting the critical temperatures and critical exponents of three-dimensional Ising models. We analyze the low temperature magnetization as well as high temperature susceptibility series of simple cubic, body-centered cubic, face-centered cubic and diamond lattices, using two different variables for the inverse critical temperature. In the case of simple cubic lattices, the magnetization series was modified to deduce accurate values of the critical temperatures. The alternate variable for dimensionless inverse temperature suggested by Guttmann and Thompson has also been employed for the estimation of the critical parameters.