172 research outputs found
Gibbs free energy and Helmholtz free energy for a three-dimensional Ising-like model
The critical behavior of a 3D Ising-like system is studied at the microscopic
level of consideration. The free energy of ordering is calculated analytically
as an explicit function of temperature, an external field and the initial
parameters of the model. Within a unified approach, both Gibbs and Helmholtz
free energies are obtained and the dependencies of them on the external field
and the order parameter, respectively, are presented graphically. The regions
of stability, metastability, and unstability are established on the order
parameter-temperature plane. The way of implementation of the well-known
Maxwell construction is proposed at microscopic level.Comment: 10 pages, 4 figure
Phase transition in a cell fluid model
We propose a method of describing a phase transition in a cell fluid model
with pair interaction potential that includes repulsive and attractive parts.
An exact representation of the grand partition function of this model is
obtained in the collective variables set. The behavior of the system at
temperatures below and above the critical one is explored in the approximation
of a mean-field type. An explicit analytic form of the equation of state which
is applicable in a wide range of temperatures is derived, taking into account
an equation between chemical potential and density. The coexistence curve, the
surface of the equation of state and the phase diagram of the cell Morse fluid
are plotted.Comment: 18 pages, 12 figure
A non-classical van der Waals loop: Collective variables method
The equation of state is investigated for an Ising-like model in the
framework of collective variables method. The peculiar feature of the theory is
that a non-classical van der Waals loop is extracted. The results are compared
with the ones of a trigonometric parametric model in terms of normalized
magnetization, \tilde{M}, and field, \tilde{H}.Comment: 9 pages, 2 figure
The equation of state of a cell fluid model in the supercritical region
The analytic method for deriving the equation of state of a cell fluid model
in the region above the critical temperature () is
elaborated using the renormalization group transformation in the collective
variables set. Mathematical description with allowance for non-Gaussian
fluctuations of the order parameter is performed in the vicinity of the
critical point on the basis of the model. The proposed method of
calculation of the grand partition function allows one to obtain the equation
for the critical temperature of the fluid model in addition to universal
quantities such as critical exponents of the correlation length. The isothermal
compressibility is plotted as a function of density. The line of extrema of the
compressibility in the supercritical region is also represented.Comment: 26 pages, 6 figures, 1 tabl
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