Related papers: Potts Partition Function Zeros and Ground State En…
We study the zero-temperature partition function of the Potts antiferromagnet (i.e., the chromatic polynomial) on a torus using a transfer-matrix approach. We consider square- and triangular-lattice strips with fixed width L, arbitrary…
We study the antiferromagnetic $q$-state Potts model on the square lattice for $q=3$ and $q=4$, using the Wang-Swendsen-Koteck\'y Monte Carlo algorithm and a new finite-size-scaling extrapolation method. For $q=3$ we obtain good control up…
We present exact calculations of the chromatic polynomial and resultant ground state entropy of the $q$-state Potts antiferromagnet on lattice strips that are homeomorphic expansions of a strip of the kagome lattice. The dependence of the…
We have studied the ordering of the q-colours Potts model in two dimensions on a square lattice. On the basis of our observations we propose that if q is large enough the system is not able to break global and local null magnetisation…
We compute the critical polymials for the q-state Potts model on all Archimedean lattices, using a parallel implementation of the algorithm of (Jacobsen, J. Phys. A: Math. Theor. 47 135001) that gives us access to larger sizes than…
We study the partition function of Potts model in an external (magnetic) field, and its connections with the zero-field Potts model partition function. Using a deletion-contraction formulation for the partition function Z for this model, we…
Let $Z_n(z,t)$ denote the partition function of the $q$-state Potts Model on the rooted binary Cayley tree of depth~$n$. Here, $z = {\rm e}^{-h/T}$ and $t = {\rm e}^{-J/T}$ with $h$ denoting an externally applied magnetic field, $T$ the…
We present an analytic study of the Potts model partition function on two different types of self-similar lattices of triangular shape with non integer Hausdorff dimension. Both types of lattices analyzed here are interesting examples of…
Here we observe that list coloring in graph theory coincides with the zero-temperature antiferromagnetic Potts model with an external field. We give a list coloring polynomial that equals the partition function in this case. This is…
We apply a newly proposed Monte Carlo method, the Wang-Landau algorithm, to the study of the three-dimensional antiferromagnetic q-state Potts models on a simple cubic lattice. We systematically study the phase transition of the models with…
We present an efficient quantum algorithm for the exact evaluation of either the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function Z for a family of graphs related to irreducible cyclic codes. This problem is…
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…
We consider the Potts model with $q$ colors on a sequence of weighted graphs with adjacency matrices $A_n$, allowing for both positive and negative weights. Under a mild regularity condition the mean-field prediction for the log partition…
We study the phase diagram of the ferromagnetic $q$-state Potts model on the various three-dimensional lattices for integer and non-integer values of $q>1$. Our approach is based on a thermodynamically self-consistent Ornstein-Zernike…
We study the $q$-state Potts antiferromagnet with $q=3$ on the honeycomb lattice. Using an analytic argument together with a Monte Carlo simulation, we conclude that this model is disordered for all $T \ge 0$. We also calculate the ground…
We construct the exact partition function of the Potts model on a complete graph subject to external fields with linear and nematic type couplings. The partition function is obtained as a solution to a linear diffusion equation and the free…
In previous work with Scullard, we defined a graph polynomial P_B(q,T) that gives access to the critical temperature T_c of the q-state Potts model on a general two-dimensional lattice L. It depends on a basis B, containing n x m unit cells…
We study partition functions for the dimer model on families of finite graphs converging to infinite self-similar graphs and forming approximation sequences to certain well-known fractals. The graphs that we consider are provided by actions…
The $q$-state Potts model has stood at the frontier of research in statistical mechanics for many years. In the absence of a closed-form solution, much of the past efforts have focused on locating its critical manifold, trajectory in the…
We calculate rigorous lower bounds for the ground state degeneracy per site, $W$, of the $q$-state Potts antiferromagnet on slabs of the simple cubic lattice that are infinite in two directions and finite in the third and that thus…