Related papers: Exact solution of a two-dimensional (2D) Ising mod…
The common feature for a nontrivial hard problem is the existence of nontrivial topological structures, non-planarity graphs, nonlocalities, or long-range spin entanglements in a model system with randomness. For instance, the Boolean…
Finite-range interacting spin models are the simplest models to study the effect of beyond nearest-neighbour interactions and access new effects caused by the range of the interactions. Recent experiments have reached the regime of dominant…
Using the Trace Minimization Algorithm, we carried out an exact calculation of entanglement in a 19-site two-dimensional transverse Ising model. This model consists of a set of localized spin-1/2 particles in a two dimensional triangular…
The stacking problem is approached by computational mechanics, using an Ising next nearest neighbor model. Computational mechanics allows to treat the stacking arrangement as an information processing system in the light of a symbol…
Form factor representation of the correlation function of the 2D Ising model on a cylinder is generalized to the case of arbitrary disposition of correlating spins. The magnetic susceptibility on a lattice, one of whose dimensions ($N$) is…
Two kinds of recursive lattices with the same coordination number but different unit cells (2-D square and 3-D cube) are constructed and the antiferromagnetic Ising model is solved exactly on them to study the stable and metastable states.…
As a prelude to what might be expected as forthcoming breakthroughs in finding new approaches toward solving three-dimensional lattice models in the twenty-first century, we review the exact solutions of two lattice models in three…
Finite size effects for the Ising Model coupled to two dimensional random surfaces are studied by exploiting the exact results from the 2-matrix models. The fixed area partition function is numerically calculated with arbitrary precision by…
We analyze changes in the thermodynamic properties of a spin system when it passes from the classical two-dimensional Ising model to the spin glass model, where spin-spin interactions are random in their values and signs. Formally, the…
Accurate numerical results are presented for the three-dimensional equivalent-neighbor model on a cubic lattice, for twelve different interaction ranges (coordination number between 18 and 250). These results allow the determination of the…
We review some aspects of the fermionic interpretation of the two-dimensional Ising model. The use is made of the notion of the integral over the anticommuting Grassmann variables. For simple and more complicated 2D Ising lattices, the…
The two-dimensional Ising model on a distorted Kagom\'{e} lattice is studied by means of exact solutions and the tensor renormalisation group (TRG) method. The zero-field phase diagrams are obtained, where three phases such as…
We compute the spectrum and several critical amplitudes of the two dimensional Ising model in a magnetic field with the transfer matrix method. The three lightest masses and their overlaps with the spin and the energy operators are computed…
We study the 2D Ising model on three different types of lattices that are topologically equivalent to spheres. The geometrical shapes are reminiscent of the surface of a pillow, a 3D cube and a sphere, respectively. Systems of volumes…
The correlation function of two dimensional Ising model with the nearest neighbours interaction on the finite size lattice with the periodical boundary conditions is derived. The expressions similar to the form factor representation are…
In 2002 Biskup et al. [Europhys. Lett. 60, 21 (2002)] sketched a rigorous proof for the behavior of the 2D Ising lattice gas, at a finite volume and a fixed excess \delta M of particles (spins) above the ambient gas density (spontaneous…
Using exact results, we determine the complex-temperature phase diagrams of the 2D Ising model on three regular heteropolygonal lattices, $(3 \cdot 6 \cdot 3 \cdot 6)$ (kagom\'{e}), $(3 \cdot 12^2)$, and $(4 \cdot 8^2)$ (bathroom tile),…
We study the thermodynamical observables of the 2d Ising model in the neighborhood of the magnetic axis by means of numerical diagonalization of the transfer matrix. In particular, we estimate the leading order corrections to the…
We study mappings between distinct classical spin systems that leave the partition function invariant. As recently shown in [Phys. Rev. Lett. 100, 110501 (2008)], the partition function of the 2D square lattice Ising model in the presence…
In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact…