Related papers: Partition functions of two-dimensional Ising model…

We have studied numerically the appearance of multiscaling behavior in the three-dimensional ferromagnetic Ising site diluted model, in the form of a multifractal distribution of the decay exponents for the spatial correlation functions at…

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…

In this paper, we provide a proof of the explicit formula for the partition function of the Ising model on the Sierpinski gasket. Additionally, we demonstrate the dynamic behavior of the zero distribution of the partition function when a…

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…

It is well known that the partition function of two-dimensional Ising model can be expressed as a Grassmann integral over the action bilinear in Grassmann variables. The key aspect of the proof of this equivalence is to show that all…

We consider Ising models defined on periodic approximants of aperiodic graphs. The model contains only a single coupling constant and no magnetic field, so the aperiodicity is entirely given by the different local environments of neighbours…

We consider the Nambu-Goto bosonic string model as a description of the physics of interfaces. By using the standard covariant quantization of the bosonic string, we derive an exact expression for the partition function in dependence of the…

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…

In this paper, we consider Ising models with ferromagnetic pair interactions. We prove that the Ursell functions $u_{2k}$ satisfy: $(-1)^{k-1}u_{2k}$ is increasing in each interaction. As an application, we prove a 1983 conjecture by…

We perform the calculation of the partition function of the Poisson-sigma model on the world sheet with the topology of a two-dimensional disc. Considering the special case of a linear Poisson structure we recover the partition function of…

We develop a field theoretical approach to the classical two-dimensional models, particularly to 2D Ising model (2DIM) and $XYZ$ model, which is simple to apply for calculation of various correlation functions. We calculate the partition…

A wide class of problems in combinatorics, computer science and physics can be described along the following lines. There are a large number of variables ranging over a finite domain that interact through constraints that each bind a few…

The ferromagnet-to-paramagnet transition of the four-dimensional random-field Ising model with Gaussian distribution of the random fields is studied. Exact ground states of systems with sizes up to 32^4 are obtained using graph theoretical…

Recent work on local functional theories of critical inhomogeneous fluids and Ising-like magnets has shown them to be a potentially exact, or near exact, description of universal finite-size effects associated with the excess free-energy…

We consider the ratio of two Gauss hypergeometric functions, in which the parameters of the numerator function differ from the respective parameters of the denominator function by integers. We derive explicit integral representations for…

We compute the exact partition function, the universal ground state degeneracy and boundary state of the 2-D Ising model with boundary magnetic field at off-critical temperatures. The model has a domain that exhibits states localized near…

The partition function of four dimensional Euclidean, non-supersymmetric SU(2) Yang--Mills theory is calculated in the perturbative and weak coupling regime i.e. in a small open ball about the flat connection (what we call the vicinity of…

A Green's function formalism is used to calculate the spectrum of excitations of two neighboring impurities implanted in a semi-infinite ferromagnetic. The equations of motion for the Green's functions are determined in the framework of the…

We show that the two dimensional Ising model is complete, in the sense that the partition function of any lattice model on any graph is equal to the partition function of the 2D Ising model with complex coupling. The latter model has all…

Non-Gaussian likelihoods, ubiquitous throughout cosmology, are a direct consequence of nonlinearities in the physical model. Their treatment requires Monte-Carlo Markov-chain or more advanced sampling methods for the determination of…