Related papers: Partition function and magnetization of two-dimens…
The exact partition function of the two-dimensional nearest neighbour Ising model pertaining to square lattices is derived for N sites in the case of a non-vanishing magnetic field.When the magnetic field is zero,the partition functions…
Employing the exact solution of Onsager for two-dimensional Ising models, simple expressions are proposed for computing the partition function, magnetization, specific heat and susceptibility for non-zero magnetic fields of square lattices.…
The partition function and magnetization equations are derived for the two-dimensional nearest neighbour Ising models in a magnetic field.
The partition functions for two-dimensional nearest neighbour Ising model in a non-zero magnetic field have been derived for finite square lattices with the help of graph theoretical procedures, show-bit algorithm, enumeration of…
Using a combinatorial method, the partition functions for two-dimensional nearest neighbour Ising models have been derived for a square lattice of 16 sites in the presence of the magnetic field. A novel hierarchical method of enumeration of…
The zero-field partition function of two-dimensional nearest neighbor Ising models of square lattices is derived in terms of the generalized hypergeometric series by evaluating the integral in the exact solution of Onsager. An approximate…
There is no an accepted exact partition function (PF) for the two-dimensional (2D) Ising model with a non-zero external magnetic field to our knowledge. Here we infer an empirical PF for such an Ising model. We compare the PFs for two…
The partition function of two-dimensional nearest neighbour Ising models in a non-zero magnetic field is derived employing a matrix formulation.
The partition function of the two-dimensional Ising model with zero magnetic field on a square lattice with m x n sites wrapped on a torus is computed within the transfer matrix formalism in an explicit step-by-step approach inspired by…
The two-dimensional Ising model is representable as a lattice free-fermion field theory in terms of the integral over anticommuting Grassmann variables. The exact solution in a zero magnetic field then follows by evaluating Gaussian…
An explicit expression for the partition function of two-dimensional nearest neighbour Ising models in the presence of a magnetic field is derived by a systematic enumeration of all the spin configurations pertaining to a square lattice of…
There is no an exact solution to three-dimensional (3D) finite-size Ising model (referred to as the Ising model hereafter for simplicity) and even two-dimensional (2D) Ising model with non-zero external field to our knowledge. Here by using…
The partition function for two-dimensional nearest neighbour Ising models in the presence of a magnetic field is derived . A comparison with the partition functions predicted by Onsager is carried out. The critical temperature estimated by…
Employing heuristic susceptibility equations in conjunction with the well-known critical exponents, the magnetization and partition function for two-dimensional nearest neighbour Ising models are formulated in terms of the Gauss…
We conjecture an approximate expression for the free energy in the thermodynamic limit of the classical square lattice Ising model in a uniform (real) magnetic field. The zero-field result is well known due to Onsager for more than eighty…
We represent a general procedure for calculating the partition function of an Ising model on a one dimensional Fibonacci lattice in presence of magnetic field.This partition function can be written as a sum of partition functions of usual…
We propose a method for generalizing the Ising model in magnetic fields and calculating the partition function (exact solution) for the Ising model of an arbitrary shape. Specifically, the partition function is calculated using matrices…
A method is proposed for exactly calculating the partition function of a rectangular Ising lattice with the presence of a uniform external field. This approach is based on the method of the transfer matrix developed about seventy years ago…
We present calculations of the complex-temperature zeros of the partition functions for 2D Ising models on the square lattice with spin $s=1$, 3/2, and 2. These give insight into complex-temperature phase diagrams of these models in the…
We study the two-dimensional square lattice Ising ferromagnet and antiferromagnet with a magnetic field by using tensor network method. Focusing on the role of guage fixing, we present the partition function in terms of a tensor network.…