The microcanonical transfer matrix is used to study the distribution of the Fisher zeros of the Q > 2 Potts models in the complex temperature plane with nonzero external magnetic field Hq. Unlike the Ising model for Hq 6= 0 which has only a non-physical critical point (the Fisher edge singularity), the Q > 2 Potts models have physical critical points forHq < 0 as well as the Fisher edge singula...

We prove that the spectral gap of the Swendsen-Wang process for the Potts model on graphs with bounded degree is bounded from below by some constant times the spectral gap of any single-spin dynamics. This implies rapid mixing for the two-dimensional Potts model at all temperatures above the critical one, as well as rapid mixing at the critical temperature for the Ising model. After this we int...

We demonstrate that the τ (j)-matrices in the superintegrable chiral Potts model possess the Onsager algebra symmetry for their degenerate eigenvalues. The Fabricius-McCoy comparison of functional relations of the eight-vertex model for roots of unity and the superintegrable chiral Potts model has been carefully analyzed by identifying equivalent terms in the corresponding equations, by which w...

The two-point correlation function of a Potts model on a graph G may be expressed in terms of the flow polynomials of ‘Poissonian’ random graphs derived from G by replacing each edge by a Poissondistributed number of copies of itself. This fact extends to Potts models the so-called random-current expansion of the Ising model.

The q = 10 and q = 200 state Potts models coupled to 2d gravity are investigated numerically and shown to have continuous phase transitions, contrary to their behavior on a regular lattice. Critical exponents are extracted and possible critical behavior for general q-state Potts models coupled to gravity is discussed.

The Yang-Lee, Fisher and Potts zeros of the one-dimensional Q-state Potts model are studied using the theory of dynamical systems. An exact recurrence relation for the partition function is derived. It is shown that zeros of the partition function may be associated with neutral fixed points of the recurrence relation. Further, a general equation for zeros of the partition function is found and ...

We propose a generalisation of the q-state Potts model in which two neighbouring spins in states s and s' have a coupling -J$( s, s'), and develop an exact graphical expansion of the partition function where each cluster in the graph can be coloured in one of C 6 q colours. This spin model reduces to the standard Potts model (one colour) when J , = J ; it also encompasses many new applications ...

Inverse statistical approaches to determine protein structure and function from Multiple Sequence Alignments (MSA) are emerging as powerful tools in computational biology. However the underlying assumptions of the relationship between the inferred effective Potts Hamiltonian and real protein structure and energetics remain untested so far. Here we use lattice protein model (LP) to benchmark tho...

We obtain the critical threshold for a host of Potts and percolation models on lattices having a structure which permits a duality consideration. The consideration generalizes the recently obtained thresholds of Scullard and Ziff for bond and site percolation on the martini and related lattices to the Potts model and to other lattices.