Related papers: Ising model on nonorientable surfaces: Exact solut…
We study the finite-size scaling properties of the Ising model on the Moebius strip and the Klein bottle. The results are compared with those of the Ising model under different boundary conditions, that is, the free, cylindrical, and…
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…
Ising models with nearest-neighbor ferromagnetic random couplings on a square lattice with a (1,1) surface are studied, using Monte Carlo techniques and star-tiangle transformation method. In particular, the critical exponent of the surface…
The partition function of the square lattice Ising model on the rectangle with open boundary conditions in both directions is calculated exactly for arbitrary system size $L\times M$ and temperature. We start with the dimer method of…
Based on the results obtained in [Hucht, J. Phys. A: Math. Theor. 50, 065201 (2017)], we show that the partition function of the anisotropic square lattice Ising model on the $L \times M$ rectangle, with open boundary conditions in both…
We simulate the spin-1/2 Ising model and the Blume-Capel model at various values of the parameter D on the simple cubic lattice. We perform a finite size scaling study of lattices of a linear size up to L=360 to obtain accurate estimates…
In the present paper, we proposed a simple spin-1/2 model which provides a exactly solvable example to study the Ising criticality with central charge c=1/2. By mapping it onto the real Majorana fermions, the Ising critical behavior is…
The ordering of charges on half-filled hypercubic lattices is investigated numerically, where electroneutrality is ensured by background charges. This system is equivalent to the $s = 1/2$ Ising lattice model with antiferromagnetic $1/r$…
Let f, U and C represent, respectively, the free energy, the internal energy and the specific heat of the critical Ising model on the square M x N lattice with periodic boundary conditions. We find that N f and U are well-defined odd…
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…
We investigate three Ising models on the simple cubic lattice by means of Monte Carlo methods and finite-size scaling. These models are the spin-1/2 Ising model with nearest-neighbor interactions, a spin-1/2 model with nearest-neighbor and…
Consider the Ising model on $([1,2N]\times[1,2M])\cap\mathbb{Z}^2$ at critical temperature with periodic boundary condition in the horizontal direction and free boundary condition in the vertical direction. Let $E_{M,N}$ be its total energy…
We study the two-dimensional critical Ising model on a M\"obius strip based on a duality relation between conformally invariant boundary conditions. By using a Majorana fermion field theory, we obtain explicit representations of crosscap…
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…
The critical properties of an infinitely long Ising strip with finite width L joined periodically or antiperiodically are investigated by analyzing the distribution of partition function zeros. For periodic boundary condition, the the…
The Ising model in two dimensions with special toroidal boundary conditions is analyzed. These boundary condition, which we call duality twisted boundary conditions, may be interpreted as inserting a specific defect line ("seam") in the…
Closed-form expressions are obtained for the generating function of close-packed dimers on a $2M \times 2N$ simple quartic lattice embedded on a M\"obius strip and a Klein bottle. Finite-size corrections are also analyzed and compared with…
Using the bond-propagation algorithm, we study the Ising model on a rectangle of size $M \times N$ with free boundaries. For five aspect ratios $\rho=M/N=1,2,4,8,16$, the critical free energy, internal energy and specific heat are…
We study the spin-$1/2$ Ising chain with multispin interactions $K$ involving the product of $m$ successive spins, for general values of $m$. Using a change of spin variables the zero-field partition function of a finite chain is obtained…
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…