Free energy and equation of state of Ising-like magnet near the critical point

Abstract

The description of a three-dimensional Ising-like magnet in the presence of an external field in the vicinity of the critical point by the collective variables method is proposed. Using the renormalization group transformations, the scaling region size is defined as a function of temperature and field. The obtained expressions for the free energy, equation of state and susceptibility allow one to analyse their dependence on microscopic parameters of the system. The critical exponents of the correlation length and order parameter are calculated as well. The results agree qualitatively with ones obtained within the framework of the parametric representation of the equation of state and Monte-Carlo simulations. The calculations do not involve any parametrization, phenomenological assumptions and adjustable parameters. The approach can be extended to models with a multicomponent order parameter.

Free energy of 3D Ising-like system near the phase transition point`

“…The main contribution toγ + is formed by quantityγ 1 . One should note that similar calculations have been performed in [10]. The exit point from CR was determined in [10] as a solution of some equation.…”

“…One should note that similar calculations have been performed in [10]. The exit point from CR was determined in [10] as a solution of some equation. Therefore, the results of calculations were presented in the form of figures.…”

“…The free energy presentations (6) and (10) are basic in the scaling theory. Depending on the ratio between quantities τ and h one could use the first one or another.…”

“…Considering the relation (4) it is easy to see that there is no such a value of s which could make it possible to unify the expressions (6) and (10). They are obtained via considering diametrically opposite limiting cases.…”

“…They are obtained via considering diametrically opposite limiting cases. It turned out that it is possible to find an explicit form for the free energy using the results presented in [7][8][9][10][11]. Such a calculation employs the collective variables (CV) set [12] and it is valid for arbitrary values of the field and temperature.…”