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

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

Rapid Communication 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,M , and field,H . Recently, in [1] it was shown that considering the system of Ising spins in an external field within the collective variables (CV) method We consider a system of N Ising spins on a simple cubic lattice of spacing c. The Hamiltonian of such a system is well known Here, the spin variables σ i take on ±1, H is the external field, and Φ(r i j ) is a short-range interaction potential between spins located at the i -th and j -th sites of separation r i j . The interaction potential can be chosen in the form of exponentially decreasing function, Φ(r i j ) = const · exp (−r i j /b), with b being an effective range. The partition function Z = {σ} e −βH , where β = (k B T ) −1 is the inverse temperature, can be written in terms of collective variables ρ k Here, the quantity d(k) contains the Fourier transform of the interaction potential ForΦ(k), we use the so-called parabolic approximatio