Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Method of Calculating the Free Energy of Three-Dimensional Ising-Like
  System in an External Field with the Use of the $\rho^6$ Model   The microscopic approach to calculating the free energy of a
three-dimensional Ising-like system in a homogeneous external field is
developed in the higher non-Gaussian approximation (the $\rho^6$ model) at
temperatures above the critical value of $T_c$ ($T_c$ is the phase-transition
temperature in the absence of an external field). The free energy of the system
is found by separating the contributions from the short- and long-wave
spin-density oscillation modes taking into account both the temperature and
field fluctuations of the order parameter. Our analytical calculations do not
involve power series in the scaling variable and are valid in the whole
field-temperature plane near the critical point including the region in the
vicinity of the limiting field $\tilde h_c$, which divides external fields into
the weak and strong ones (i.e., the crossover region). In this region, the
temperature and field effects on the system are equivalent, the scaling
variable is of the order of unity, and power series are not efficient. The
obtained expression for the free energy contains the leading terms and terms
determining the temperature and field confluent corrections.

18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
2
The categories of this paper are: math