Related papers: Exact solution of rectangular Ising lattice in a u…
We study the topology dependence of finite size corrections to the Ising model partition function by considering the model on a triangular lattice embedded on a genus two surface. At criticality we observe a universal shape dependent…
A new finite-size scaling approach based on the transfer matrix method is developed to calculate the critical temperature of anisotropic two-layer Ising ferromagnet, on strips of r wide sites of square lattices. The reduced internal energy…
An integral representation of the partition function for general $n$-dimensional Ising models with nearest or non-nearest neighbours interactions is given. The representation is used to derive some properties of the partition function. An…
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…
In this paper we introduce an approximate method to solve the quantum cavity equations for transverse field Ising models. The method relies on a projective approximation of the exact cavity distributions of imaginary time trajectories…
An asymmetrical 2D Ising model with a zigzag surface, created by diagonally cutting a regular square lattice, has been developed to investigate the thermodynamics and phase transitions on surface by the methodology of recursive lattice,…
Transfer-matrix methods, with the help of finite-size scaling and conformal invariance concepts, are used to investigate the critical behavior of two-dimensional square-lattice Ising spin-1/2 systems with first- and second-neighbor…
The square lattice Ising model under the Brascamp-Kunz boundary conditions is a well-known exactly solvable lattice model. The exact solution of this system has been derived within the framework of Pfaffian-type method. In this paper we…
We introduce an exact algorithm for the computation of spin correlation functions for the two dimensional +/-J Ising spin glass in the ground state. Unlike with the transfer matrix method, there is no particular restriction on the shape of…
In this paper the exact solution and correlation functions for a double-chain Ising model with multi-spin interactions and symmetric Hamiltonian density are obtained. The study employs the transfer matrix method to derive fundamental…
Using exact partition functions and finite-size corrections for the Ising model on finite square, plane triangular, and honeycomb lattices, we obtain universal finite-size scaling functions for the specific heat, the internal energy, and…
An $n$-dimensional generalization of the Onsager Ising partition function integral is reduced to a single integral and applied to evaluate the partition function and residual entropy of an eight vertex model.
A star-triangle mapping transformation is used to establish an exact correspondence between the spin-1/2 Ising model on the Shastry-Sutherland (orthogonal-dimer) lattice and respectively, the spin-1/2 Ising model on a bathroom tile (4-8)…
The Grassmann path integral approach is used to calculate exact partition functions of the Ising model on MxN square (sq), plane triangular (pt) and honeycomb (hc) lattices with periodic-periodic (pp), periodic-antiperiodic (pa),…
A free boson on a lattice is the simplest field theory one can think of. Its partition function can be easily computed in momentum space. However, this straightforward solution hides its integrability properties. Here, we use the methods of…
We obtain the diagonal reflection matrices for a recently introduced family of dilute ${\rm A}_L$ lattice models in which the ${\rm A}_3$ model can be viewed as an Ising model in a magnetic field. We calculate the surface free energy from…
Understanding the relationship which integrable (solvable) models, all of which possess very special symmetry properties, have with the generic non-integrable models that are used to describe real experiments, which do not have the symmetry…
We develop a transfer matrix method to compute exactly the spin-spin correlation functions of Bethe lattice spin models in the external magnetic field h and for any temperature T. We first compute the correlation function for the most…
We prove that the 2D Ising model is complete in the sense that the partition function of any classical q-state spin model (on an arbitrary graph) can be expressed as a special instance of the partition function of a 2D Ising model with…
We have proposed an efficient algorithm to calculate physical quantities in the translational invariant three-dimensional tensor networks, which is particularly relevant to the study of the three-dimensional classical statistical models and…