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Ferroelectrics

Critical Behaviour of 3D Systems in the External Field

Mykhailo P. Kozlovskii

Published Jul 1, 2005• 2 citations
Publisher

Abstract

The method for calculation of the partition function of the lattice model for the magnet in the external field near critical point is proposed. The recurrence relations and their explicit solution near the critical point are found. The critical exponents for the correlation length are obtained.
DOI
10.1080/00150190590963372

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•Jan 1, 2006•0 citations
The method for calculation of the partition function of lattice model for the magnet in the external field near critical point (CP) is proposed.The recurrence relations and their explicit solution near the critical point are founded.It is shown that dependence on temperature of thermodynamic functions near CP, when the field value comes down to zero, is in good agreement with the previous results obtained using the collective variable method.The phase transition temperature (when h = 0) is calculated and the dependence on parameters of interaction potential is found.
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The present work is devoted to the investigation of the 3D Ising-like model in the presence of an external field in the vicinity of critical point.The method of collective variables is used.General expressions for the order parameter and susceptibility are calculated as functions of temperature and the external field as well as scaling functions of that are explicitly obtained.The results are compared with the ones obtained within the framework of parametric representation of the equation of state and Monte Carlo simulations.New expression for the exit point from critical regime of the order parameter fluctuations is proposed and used for the calculation.
Equation of State and Thermodynamic Functions of the Ising-like Magnet at T>TcT>T_cT>Tc​
The 3D Ising-like system in the external field is described using the non-perturbative collective variables method. The universal as well as nonuniversal system characteristics are obtained within the framework of this approach. The calculations are carried out on the microscopic level starting from the Hamiltonian. They are valid in the whole h−Th-Th−T plane of the critical region. It is established, that the contributions related with wave vector values $\vk\to0$ exhibit the properties of the total system near the critical point. The behaviour of the susceptibility as function of the temperature in the presence of the field is investigated. The locations of the maximums susceptibility on the temperature scale for different values of the field are established.
The 3D one-component spin system in an external magnetic field is studied using the collective variables method. The integration of the partition function of the system over the phase space layers is performed in the approximation of the sextic measure density including the even and the odd powers of the variable (the asymmetric ρ⁶ model). The general recurrence relations between the coefficients of the effective measure densities are obtained. The new functions appearing in these recurrence relations are given in the form of a convergent series.
The influence of a homogeneous external field on a three-dimensional uniaxial magnet behaviour near the critical point is investigated on the microscopic level by the nonperturbative collective variable (CV) method using the ρ4 model. The research is carried out in the high-temperature region. The critical exponents related with external field are calculated. The analytic explicit expressions for the free energy, average spin moment and susceptibility are obtained without using any phenomenological assumptions and adjusting parameters. The field dependences of the order parameter are plotted for the field region including the neighbourhood of the pseudocritical line. It is established that long-wave fluctuations of the order parameter are responsible for main features of the crossover between the temperature-dependence and field-dependence critical behaviour of the system. The maximum locations on the temperature scale for the long-wave part of the susceptibility are determined for different values of the field.