Related papers: Potts model on recursive lattices: some new exact …
We present exact calculations of the zero-temperature partition function for the $q$-state Potts antiferromagnet (equivalently, the chromatic polynomial) for families of arbitrarily long strip graphs of the square and triangular lattices…
The distribution of the zeros of the partition function in the complex temperature plane (Fisher zeros) of the two-dimensional Q-state Potts model is studied for non-integer Q. On $L\times L$ self-dual lattices studied ($L\le8$), no Fisher…
We show how to compute the exact partition function for lattice statistical-mechanical models whose Boltzmann weights obey a special "crossing" symmetry. The crossing symmetry equates partition functions on different trivalent graphs,…
We present exact calculations of the $q$-state Potts model partition functions and the equivalent Tutte polynomials for chain graphs comprised of $m$ repeated hammock subgraphs $H_{e_1,...,e_r}$ connected with line graphs of length $e_g$…
Any two-dimensional infinite regular lattice G can be produced by tiling the plane with a finite subgraph B of G; we call B a basis of G. We introduce a two-parameter graph polynomial P_B(q,v) that depends on B and its embedding in G. The…
It is well-known that exact enumerations of close-packed dimers can be carried out for two-dimensional lattices. While details of results are now known for most lattices, due to the unique nature of the lattice structure, there has been no…
We study the Potts model (defined geometrically in the cluster picture) on finite two-dimensional lattices of size L x N, with boundary conditions that are free in the L-direction and periodic in the N-direction. The decomposition of the…
We calculate zeros of the $q$-state Potts model partition function on $m$'th-iterate Sierpinski graphs, $S_m$, in the variable $q$ and in a temperature-like variable, $y$. We infer some asymptotic properties of the loci of zeros in the…
There is no an exact solution to three-dimensional (3D) finite-size Ising model (referred to as the Ising model hereafter for simplicity) and even two-dimensional (2D) Ising model with non-zero external field to our knowledge. Here by using…
We present exact calculations of the zero-temperature partition function for the q-state Potts antiferromagnet (equivalently, the chromatic polynomial) for two families of arbitrarily long strip graphs of the square lattice with periodic…
We present exact calculations of Potts model partition functions and the equivalent Tutte polynomials for polygon chain graphs with open and cyclic boundary conditions. Special cases of the results that yield flow and reliability…
We apply a simple analytical criterion for locating critical temperatures to Potts models on square and triangular lattices. In the self-dual case, i.e. on the square lattice we reproduce known exact values of the critical temperature and…
The zeros of the partition function of the ferromagnetic q-state Potts model with long-range interactions in the complex-q plane are studied in the mean-field case, while preliminary numerical results are reported for the finite 1d chains…
We report some new results on the complex-temperature (CT) singularities of $q$-state Potts models on the square lattice. We concentrate on the problematic region $Re(a) < 0$ (where $a=e^K$) in which CT zeros of the partition function are…
The microcanonical transfer matrix and its extensions offer a new way of obtaining exact partition functions on finite two dimensional lattices. We show the density of the partition function zeros in the complex x- plane for the Ising model…
An exact analytical solution of generalized three-state double-chain Potts model with multi-spin interactions which are invariant under cyclic shift of all spin values is obtained. The partition function in a finite cyclically closed strip…
We study the phase diagram of Q-state Potts models, for Q=4 cos^2(PI/p) a Beraha number (p>2 integer), in the complex-temperature plane. The models are defined on L x N strips of the square or triangular lattice, with boundary conditions on…
Biskup et al. [Phys. Rev. Lett. 84 (2000) 4794] have recently suggested that the loci of partition function zeroes can profitably be regarded as phase boundaries in the complex temperature or field planes. We obtain the Fisher zeroes for…
We compute the partition function of the $q$-states Potts model on a random planar lattice with $p\leq q$ allowed, equally weighted colours on a connected boundary. To this end, we employ its matrix model representation in the planar limit,…
We consider the Potts model in a magnetic field on an arbitrary graph $G$. Using a formula of F. Y. Wu for the partition function $Z$ of this model as a sum over spanning subgraphs of $G$, we prove some properties of $Z$ concerning…