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In 1952, Kac and Ward developed a combinatorial formulation for the two dimensional Ising model which is another method of obtaining Onsager's formula for the free energy per site in the thermodynamic limit of the model. Feynman gave an…
We develop a field theoretical approach to the classical two-dimensional models, particularly to 2D Ising model (2DIM) and $XYZ$ model, which is simple to apply for calculation of various correlation functions. We calculate the partition…
In our last work, we formulate a Fourier transformation on the infinite-dimensional space of functionals. Here we first calculate the Fourier transformation of infinite-dimensional Gaussian distribution $\exp(-\pi…
There is a new class of two-dimensional magnetic materials polymeric iron (III) acetate fabricated recently in which Fe ions form a star lattice. We study the thermodynamics of Ising spins on the star lattice with exact analytic method and…
The paper presents new method for calculating the low-temperature asymptotics of free energy of the 3D Ising model in external magnetic field $(H\neq 0)$. The results obtained are valid in the wide range of temperature and magnetic field…
Exact expressions for the partition functions of the rigid string and membrane at any temperature are obtained in terms of hypergeometric functions. By using zeta function regularization methods, the results are analytically continued and…
We consider a continuous-time simple symmetric random walk on the integer lattice $\mathbb{Z}^d$ in dimension $d \geq 3$, subject to a random potential given by a field of two-sided Wiener processes. In the high-temperature regime, we prove…
We study the partition function per site of the integrable $Sp(2n)$ vertex model on the square lattice. We establish a set of transfer matrix fusion relations for this model. The solution of these functional relations in the thermodynamic…
Free energy as a function of polarization is calculated for the square-lattice $J_1$-$J_2$ Ising model for $J_2 < |J_1|/2$ using the random local field approximation (RLFA) and Monte Carlo (MC) simulations. Within RLFA, it reveals a…
In this paper we investigate certain fusion relations associated to an integrable vertex model on the square lattice which is invariant under $Sp(4)$ symmetry. We establish a set of functional relations which include a transfer matrix…
We obtain an explicit expression for the multipoint energy correlations of a non solvable two-dimensional Ising models with nearest neighbor ferromagnetic interactions plus a weak finite range interaction of strength $\lambda$, in a scaling…
We study a thermodynamic potential during the classical gravitational collapse of a 4D (3+1) massless scalar field to a Schwarzschild black hole in isotropic coordinates. We track numerically the function $F(t)=-dI/dt=-L$, where $I$ is the…
The geometric frustration of the spin-1/2 Ising-Heisenberg model on the triangulated Kagome (triangles-in-triangles) lattice is investigated within the framework of an exact analytical method based on the generalized star-triangle mapping…
We formulate a quantum formalism for the statistical mechanical models of discretized field theories on lattices and then show that the discrete version of $\phi^4$ theory on 2D square lattice is complete in the sense that the partition…
We study some properties of the Ising model in the plane of the complex (energy/temperature)-dependent variable $u=e^{-4K}$, where $K=J/(k_BT)$, for nonzero external magnetic field, $H$. Exact results are given for the phase diagram in the…
A wide class of problems in combinatorics, computer science and physics can be described along the following lines. There are a large number of variables ranging over a finite domain that interact through constraints that each bind a few…
We use techniques in the shuffle algebra to present a formula for the partition function of a one-dimensional log-gas comprised of particles of (possibly) different integer charges at certain inverse temperature $\beta$ in terms of the…
We give an expression for the partition function of a one-dimensional log-gas comprised of particles of (possibly) different integer charge at inverse temperature {\beta} = 1 (restricted to the line in the presence of a neutralizing field)…
We show that the partition function for a scalar field in a static spacetime background can be expressed as a functional integral in the corresponding optical space, and point out that the difference between this and the functional integral…
The free energy and the specific heat of the two-dimensional Gaussian random bond Ising model on a square lattice are found with high accuracy using graph expansion method. At low temperatures the specific heat reveals a zero-temperature…