Related papers: Partition function for the two-dimensional square …
It is well known that the partition function of two-dimensional Ising model can be expressed as a Grassmann integral over the action bilinear in Grassmann variables. The key aspect of the proof of this equivalence is to show that all…
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…
The partition function (quantum transition amplitude) of the gauge system with gauge group $Z_2$ coupled with Majorana fermions is calculated on the regular 3D cubic lattice.
We present a dual representation of the partition function of the charged scalar field in which the complex action problem at non-zero chemical potential is absent. In this dual representation Monte Carlo simulations are possible and we…
We rigorously examine 2d-square lattices composed of classical spins isotropically coupled between first-nearest neighbours. A general expression of the characteristic polynomial associated with the zero-field partition function Zinf{N}(0)…
The Ising model on an alternating triangular lattice with the nearest-neighbor interaction in a magnetic field is presented. Exact solution of this model is found. The thermodynamic quantities, like free energy, specific heat a finite…
We present a numerical study based on Monte Carlo algorithm of the magnetic properties of a mixed Ising ferrimagnetic model on a cubic lattice where spins $\sigma =\pm 1/2$ and spins $S=0,\pm 1$ are in alternating sites on the lattice. We…
The universal scaling function of the square lattice Ising model in a magnetic field is obtained numerically via Baxter's variational corner transfer matrix approach. The high precision numerical data is in perfect agreement with the…
The partition function of a system of galaxies in gravitational interaction can be cast in an Ising Model form, and this reformulated via a Hubbard--Stratonovich transformation into a three dimensional stochastic and classical scalar field…
The Ising square lattice model with nearest-neighbor (nn) interactions ($J_1$) is one of the few exactly solvable models [1]. Adding next-neareast- neighbor (nnn) interactions ($J_2$) or a magnetic field (or both) leads to the non…
The Ising model was generalized to a system of cells interacting exclusively by presence of shared spins. Within the cells there are interactions of any complexity, the simplest intracell interactions come down to the Ising model. The…
Partition functions for non-interacting particles are known to be symmetric functions. It is shown that powerful group-theoretical techniques can be used not only to derive these relationships, but also to significantly simplify calculation…
We discuss the hard-hexagon and hard-square problems, as well as the corresponding problem on the honeycomb lattice. The case when the activity is unity is of interest to combinatorialists, being the problem of counting binary matrices with…
We prove that for the Ising model on a lattice of dimensionality $d \ge 2$, the zeros of the partition function $Z$ in the complex $\mu$ plane (where $\mu=e^{-2\beta H}$) lie on the unit circle $|\mu|=1$ for a wider range of $K_{n n'}=\beta…
We study the analytic properties of the scaling function associated with the 2D Ising model free energy in the critical domain $T \to T_c$, $H \to 0$. The analysis is based on numerical data obtained through the Truncated Free Fermion Space…
We propose an importance sampling scheme to estimate the partition function of the two-dimensional ferromagnetic Ising model and the two-dimensional ferromagnetic $q$-state Potts model, both in the presence of an external magnetic field.…
We consider the Ising model on a cylindrical lattice of L columns, with fixed-spin boundary conditions on the top and bottom rows. The spontaneous magnetization can be written in terms of partition functions on this lattice. We show how we…
We present a method to analyze magnetic properties of frustrated Ising spin models on specific hierarchical lattices with random dilution. Disorder is induced by dilution and geometrical frustration rather than randomness in the internal…
A $d$-dimensional Ising model on a lattice torus is considered. As the size $n$ of the lattice tends to infinity, a Poisson approximation is given for the distribution of the number of copies in the lattice of any given local configuration,…
We study $N=2$ supersymmetric gauge theories on a large family of squashed 4-spheres preserving $SU(2)\times U(1)\subset SO(4)$ isometry and determine the conditions under which this background is supersymmetric. We then compute the…