相关论文: Recent Developments on Ising and Chiral Potts Mode…
The finite lattice method of series expansion is generalised to the $q$-state Potts model on the simple cubic lattice. It is found that the computational effort grows exponentially with the square of the number of series terms obtained,…
We present a general method for analytically factorizing the n-fold form factor integrals $f^{(n)}_{N,N}(t)$ for the correlation functions of the Ising model on the diagonal in terms of the hypergeometric functions…
A generalized gauge invariant Ising model on random surfaces with non-trivial topology is proposed and investigated with the dual transformation. It is proved that the model is self-dual in case of a self-dual lattice. In special cases the…
We find the cross-over behavior for the spin-spin correlation function for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation approach of the perturbation series…
In this paper, we prove the conjecture for the coefficients of the two variable generating function used in our previous paper. The conjecture was tested numerically before, but its proof was lacking up to now.
The partition function with boundary conditions for various two-dimensional Ising models is examined and previously unobserved properties of conformal invariance and universality are established numerically.
Following a recent proposal for integrable theories in higher dimensions based on zero curvature, new Lorentz invariant submodels of the principal chiral model in 2+1 dimensions are found. They have infinite local conserved currents, which…
We study incidence geometries that are thin and residually connected. These geometries generalise abstract polytopes. In this generalised setting, guided by the ideas from the polytopes theory, we introduce the concept of chirality, a…
Some integral properties of Jack polynomials, hypergeometric functions and invariant polynomials are studied for real normed division algebras.
Duality relations are obtained for correlation functions of the q-state Potts model on any planar lattice or graph using a simple graphical analysis. For the two-point correlation we show that the correlation length is precisely the surface…
In view of its several involvements in various physical and mathematical contexts, 2D-fractional supersymmetry (F-susy) is once again considered in this work. We are, for instance, interested to study the three states Potts model $(k = 3)$…
We study the algebraic and geometric properties of the integral closure of different rings of functions on a real algebraic variety : the regular functions and the continuous rational functions.
In continuum mechanics, the non-centrosymmetric micropolar theory is usually used to capture the chirality inherent in materials. However when reduced to a two dimensional (2D) isotropic problem, the resulting model becomes non-chiral.…
We study half-BPS surface operators in supersymmetric gauge theories in four and five dimensions following two different approaches. In the first approach we analyze the chiral ring equations for certain quiver theories in two and three…
Integral representations of hypergeometric functions proved to be a very useful tool for studying their properties. The purpose of this paper is twofold. First, we extend the known representations to arbitrary values of the parameters and…
The $Z_N$-invariant chiral Potts model is considered as a perturbation of a $Z_N$ conformal field theory. In the self-dual case the renormalization group equations become simple, and yield critical exponents and anisotropic scaling which…
In this paper a new class of radial basis functions based on hyperbolic trigonometric functions will be introduced and studied. We focus on the properties of their generalised Fourier transforms with asymptotics. Therefore we will compute…
In the present paper, as we did previously in [7], we investigate the relations between the geometric properties of tilings and the algebraic properties of associated relational structures. Our study is motivated by the existence of…
Inclusion properties are studied for balls of the triangular ratio metric, the hyperbolic metric, the $j^*$-metric, and the distance ratio metric defined in the unit ball domain. Several sharp results are proven and a conjecture about the…
Consider the one-parameter generalizations of the logarithmic and exponential functions which are obtained from the integration of non-symmetrical hyperboles. These generalizations coincide to the one obtained in the context of…