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arXiv:1005.1032 · Journal of Physics A Mathematical and Theoretical

The equation of state of then-vector model: collective variables method

P R Kozak, Mykhailo P. Kozlovskii, Z. Usatenko

Published Nov 11, 2010• 1 citation
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Abstract

The critical behavior of the three-dimensional n -vector model in the presence of an external field is investigated. The mathematical description is performed with the collective variables method in the framework of the ρ 4 model approximation at the microscopic level without any adjustable parameters. The recurrence relations of the renormalization group as functions of the external field and temperature were found. The analytical expression for the free energy of the system for the temperatures T > T c and different n was obtained. The equation of state of the n -vector model for the general case of small and large external fields was written. The explicit form of the correspondent scaling function for different values of the order parameter was derived. The obtained results are in qualitative agreement with the data of Monte Carlo simulations.

DOI
10.1088/1751-8113/43/49/495001

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An analytic method for deriving the free energy of a three-dimensional Ising-like system near the critical point in a homogeneous external field is developed in the the ρ6 model approximation. The mathematical description proposed for temperatures T>Tc (Tc is the phase-transition temperature in the absence of an external field) is valid for fields near , where the scaling variable is of the order of unity and power series in this variable are not effective. At the limiting field , the temperature and field effects on the system in the vicinity of the critical point are equivalent. The total free energy is obtained as a function of temperature, field and microscopic parameters of the system without using series expansions in the scaling variable. In addition to leading terms, the expression for the free energy includes the terms determining the temperature and field confluent corrections.
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.
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Equation of State and Thermodynamic Functions of the Ising-like Magnet at T>TcT>T_cT>Tc​
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