Related papers: Partition function for several Ising model interfa…
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 derive an exact path integral formulation for the partition function for the Ising model using a mapping between spins and poles of a Laurent expansion for a field on the complex plane. The advantage in using this formulation for the…
We study phase separation in two dimensions in the scaling limit below criticality. The general form of the magnetization profile as the volume goes to infinity is determined exactly within the field theoretical framework which explicitly…
We contribute to the mathematical theory of the design of low temperature Ising machines, a type of experimental probabilistic computing device implementing the Ising model. Encoding the output of a function in the ground state of a…
The high-performance scalable parallel algorithm for rigorous calculation of partition function of lattice systems with finite number Ising spins was developed. The parallel calculations run by C++ code with using of Message Passing…
The ensemble-switch method for computing wall excess free energies of condensed matter is extended to estimate the interface free energies between coexisting phases very accurately. By this method, system geometries with linear dimensions…
An efficient Monte Carlo method is extended to evaluate directly domain-wall free-energy for randomly frustrated spin systems. Using the method, critical phenomena of spin-glass phase transition is investigated in 4d +/-J Ising model under…
The partition function of the 2D Ising model coupled to an external magnetic field is studied. We show that the sum over the spin variables can be reduced to an integration over a finite number of variables. This integration must be…
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…
While the Ising model remains essential to understand physical phenomena, its natural connection to combinatorial reasoning makes it also one of the best models to probe complex systems in science and engineering. We bring a computational…
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…
The problem of N interacting spins on a lattice is equivalent to one of N clusters linked in a specific manner. The energy of any configuration of spins can be expressed in terms of the energy levels of this cluster. A new expression is…
For the generalized Ising models with all possible interactions within a face of the square lattice the formulas for finding partition function and free energy per lattice site in the thermodynamic limit were derived on a certain, in the…
Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal…
We discuss the problem of partitioning a macroscopic system into a collection of independent subsystems. The partitioning of a system into replica-like subsystems is nowadays a subject of major interest in several field of theoretical and…
The replica method has been used to calculate the interface free energy associated with the change from periodic to anti-periodic boundary conditions in finite-dimensional spin glasses. At mean-field level the interface free energy vanishes…
We show that, above the critical temperature, if the dimension D of a given Ising spin glass model is sufficiently high, its free energy can be effectively expressed through the free energy of a related Ising model. When, in a large sense,…
This paper describes a path integral formulation of the free energy principle. The ensuing account expresses the paths or trajectories that a particle takes as it evolves over time. The main results are a method or principle of least action…
We present detailed calculations for the partition function and the free energy of the finite two-dimensional square lattice Ising model with periodic and antiperiodic boundary conditions, variable aspect ratio, and anisotropic couplings,…
The ground state energy and entropy of the dilute mean field Ising model is computed exactly by a single order parameter. An analogous exact solution is obtained in presence of a magnetic field with random locations. Results allow for a…