相关论文: Recent Developments on Ising and Chiral Potts Mode…
In the study of pattern formation in symmetric physical systems a 3-dimensional structure in thin domains is often modelled as 2-dimensional one. We are concerned with functions in $R^3$ that are invariant under the action of a…
It is well-known that many three-dimensional chiral material models become non-chiral when reduced to two dimensions. Chiral properties of the two-dimensional model can then be restored by adding appropriate two-dimensional chiral terms. In…
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…
The Potts conformal field theory is an analytic continuation in the central charge of conformal field theory describing the critical two-dimensional $Q$-state Potts model. Four-point functions of the Potts conformal field theory are…
The new integrable systems associated to the space of elliptic branched coverings are constructed. The relationship of these systems with elliptic Schlesinger's system is described. For the standard two-fold elliptic coverings the…
Some aspects of differential and integral calculi on generalized grassmann (paragrassmann) algebras are considered. The integration over paragrassmann variables is applied to evaluate the partition function for the $Z_{p+1}$ Potts model on…
This paper deals with the evaluation of some definite Euler-type integrals in terms of the Wright hypergeometric function. We obtain a theorem on the Wright hypergeometric function and then use this theorem to evaluate some definite…
We describe deformations of non-linear (birational) representations of discrete groups generated by involutions, having their origin in the theory of the symmetric five-state Potts model. One of the deformation parameters can be seen as the…
In 3 dimensions, the Ising model is in the same universality class as $\phi^4$-theory, whose massive 3-loop tetrahedral diagram, $C^{Tet}$, was of an unknown analytical nature. In contrast, all single-scale 4-dimensional tetrahedra were…
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…
A geometric picture of conformally invariant mechanics is presented. Although the standard form of the model is recovered, the careful analysis of global geometry of phase space leads to the conclusion that, in the attractive case, the…
We build the Z$_{3}$ invariants fusion rules associated to the (D$_{4}$,A$_{6}$) conformal algebra. This algebra is known to describe the tri-critical Potts model. The 4-pt correlation functions of critical fields are developed in the…
The computation of the partition function of supersymmetric gauge theories on compact manifolds can be reduced to matrix integrals by using the supersymmetric localization technique. Such matrix integrals in the case of three-dimensional…
The recursion relations of hierarchical models are studied and contrasted with functional renormalisation group equations in corresponding approximations. The formalisms are compared quantitatively for the Ising universality class, where…
In a recent paper we introduced two Potts-like models in three dimensions, which share the following properties: (A) One of the ice rules is always fulfilled (in particular also at infinite temperature). (B) Both ice rules hold for…
The magnetic properties of the antiferromagnetic Potts model with two-site interaction and the antiferromagnetic Ising model with three-site interaction on recursive lattices have been studied. A cyclic period-3 window has been revealed by…
Spin-glass and chiral-glass orderings of a three-dimensional isotropic Heisenberg spin glass are studied both by equilibrium and off-equilibrium Monte Carlo simulations with emphasis on their dynamical aspects. The model is found to exhibit…
A class of generalized Ising models is examined with a view to extracting a low energy sector comprising Dirac fermions coupled to Yang-Mills vectors. The main feature of this approach is a set of gap equations, covariant with respect to…
This is a Response to a recent Comment [F.Y. Wu et al., Phil. Mag. 88, 3093 (2008), arXiv:0811.3876] on the conjectured solution of the three-dimensional (3D) Ising model [Z.D. Zhang, Phil. Mag. 87, 5309 (2007), arXiv:0705.1045]. Several…
An overview of the mathematical structure of the three-dimensional (3D) Ising model is given, from the viewpoints of topologic, algebraic and geometric aspects. By analyzing the relations among transfer matrices of the 3D Ising model,…