The storage capacity of the Hopfield model is about 15% of the network size. It can be increased significantly in the Potts-glass model of the associative memory only. In this model neurons can be in more than two different states. We show that even greater storage capacity can be achieved in the parametrical neural network (PNN) that is based on the parametrical four-wave mixing process that i...

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 around the conformal field theories representing the pure models. We obtain a crossover in the amplitude for the correlation function for the Ising model which d...

We study two widely used algorithms, Glauber dynamics and the Swendsen-Wang algorithm, on rectangular subsets of the hypercubic lattice Z. We prove that under certain circumstances, the mixing time in a box of side length L with periodic boundary conditions can be exponential in L. In other words, under these circumstances, the mixing in these widely used algorithms is not rapid; instead, it is...

The q-state Potts model on the triangular lattice with nearest-neighbour interactions and three-site interactions in half of the triangular faces is considered. The exact duality relation is re-examined from the point of view of determining its critical point. Using the continuity and uniqueness arguments we determine the exact critical point in the ferromagnetic model. It is argued that a tran...