Behaviour of the order parameter of the simple magnet in an external field

Abstract

The effect of a homogeneous external field on the three-dimensional uniaxial magnet behaviour near the critical point is investigated within the framework of the nonperturbative collective variables method using the ρ 4 model. The research is carried out for the low-temperature region. The analytic explicit expressions for the free energy, average spin moment and susceptibility are obtained for weak and strong fields in comparison with the field value belonging to the pseudocritical line. The calculations are performed on the microscopic level without any adjusting parameters. It is established that the long-wave fluctuations of the order parameter play a crucial role in forming a crossover between the temperature-dependence and fielddependence critical behaviour of the system.

Free Energy of Three-Dimensional Uniaxial Magnet in the Higher Non-Gaussian Approximation and in the Presence of an External Field

“…Our results accord with the results obtained within the framework of the parametric representation of the equation of state [30] and Monte Carlo simulations [31]. The expressions for the thermodynamic characteristics of the system in the presence of an external field have already been obtained on the basis of the simplest non-Gaussian measure density (the ρ 4 model) in [32][33][34][35] using the point of exit of the system from the critical regime as a function of the temperature (the weak-field region) or of the field (the strong-field region). In [32,33], the thermodynamic characteristics are presented in the form of series expansions in the variables, which are combinations of the temperature and field.…”

“…In [32,33], the thermodynamic characteristics are presented in the form of series expansions in the variables, which are combinations of the temperature and field. Our calculations in the ρ 4 model approximation were also performed for temperatures T > T c [34] and T < T c [35] without using similar expansions for the roots of cubic equations appearing in the theoretical analysis. In this paper, the free energy of a 3D uniaxial magnet within the framework of the more complicated ρ 6 model is found introducing the generalized point of exit of the system from ISRN Condensed Matter Physics 3 the critical regime.…”

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

“…The detail procedure for obtaining this expression is given in [13]. Calculating the integral I np+1 with respect to the variables η k at k = 0 in the Gaussian approximation and returning to the variable ρ 0 , we obtain…”

“…In the mentioned papers as well as in [13], the size of the scaling region has been defined only by the temperature or by the field. In additional to even powers of CV, the effective Hamiltonian has contained the odd part represented by the linear and cubic terms, which are related to the presence of the field.…”

Calculation of free energy of a three-dimensional Ising-like system in an external field with the use of the model

“…The expressions for the thermodynamic characteristics of the system in the presence of an external field have already been obtained on the basis of the simplest non-Gaussian measure density (the ρ 4 model) in [19][20][21][22] using the point of exit of the system from the critical regime as a function of the temperature (the weak-field region) or of the field (the strong-field region). In [19,20], the thermodynamic characteristics are presented in the form of series expansions in the variables, which are combinations of the tempera-ture and field.…”