Related papers: Sums of Random Matrices and the Potts Model on Ran…
Duality relations are obtained for correlation functions of the q-state Potts model on any planar lattice or graph using a simple graphical analysis. For the two-point correlation we show that the correlation length is precisely the surface…
The properties of the partition function zeros in the complex temperature plane (Fisher zeros) and in the complex $Q$ plane (Potts zeros) are investigated for the $Q$-state Potts model in an arbitrary nonzero external magnetic field $H_q$,…
Different models are proposed to understand magnetic phase transitions through the prism of competition between the energy and the entropy. One of such models is a $q$-state Potts model with invisible states. This model introduces $r$…
An emerging trend in approximate counting is to show that certain `low-temperature' problems are easy on typical instances, despite worst-case hardness results. For the class of regular graphs one usually shows that expansion can be…
The vicinity of the critical point of the three-state Potts model on a Kagom\'e lattice is studied by mean of Random Matrix Theory. Strong evidence that the critical point is integrable is given.
In this paper, we study two problems related to planar matchings in random bipartite graphs. First, we colour each edge of the complete bipartite graph $K_{n,n}$ uniformly randomly from amongst ${r}$ colours and show that if ${r}$ grows…
For many systems with quenched disorder the study of ground states can crucially contribute to a thorough understanding of the physics at play, be it for the critical behavior if that is governed by a zero-temperature fixed point or for…
We give an FPTAS and an efficient sampling algorithm for the high-fugacity hard-core model on bounded-degree bipartite expander graphs and the low-temperature ferromagnetic Potts model on bounded-degree expander graphs. The results apply,…
The investigation of colour symmetries for periodic and aperiodic systems consists of two steps. The first concerns the computation of the possible numbers of colours and is mainly combinatorial in nature. The second is algebraic and…
We present an efficient algorithm for computing the partition function of the q-colouring problem (chromatic polynomial) on regular two-dimensional lattice strips. Our construction involves writing the transfer matrix as a product of sparse…
We present exact calculations of the zero-temperature partition function (chromatic polynomial) and the (exponent of the) ground-state entropy $S_0$ for the $q$-state Potts antiferromagnet on families of cyclic and twisted cyclic (M\"obius)…
In this paper, we give a sampling algorithm for the Potts model using Markov chains. Based on the sampling algorithm, we give \emph{FPRAS}es for the Potts model and the number of $k$-colorings of the graph.
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…
The zero-temperature $q$-state Potts model partition function for a lattice strip of fixed width $L_y$ and arbitrary length $L_x$ has the form $P(G,q)=\sum_{j=1}^{N_{G,\lambda}}c_{G,j}(\lambda_{G,j})^{L_x}$, and is equivalent to the…
We investigate the problem of strong spatial mixing of $q$-colorings on Bethe lattices. By analyzing the sum-product algorithm we establish the strong spatial mixing of $q$-colorings on $(b+1)$-regular Bethe lattices, for $q \geq 1+\lceil…
Through Monte Carlo simulations we study two-dimensional Potts models with $q=4, 6$ and 8 states on Voronoi-Delaunay random lattice. In this study, we assume that the coupling factor $J$ varies with the distance $r$ between the first…
In a recent paper we derived the free energy or partition function of the $N$-state chiral Potts model by using the infinite lattice ``inversion relation'' method, together with a non-obvious extra symmetry. This gave us three recursion…
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…
We derive some new structural results for the transfer matrix of square-lattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal…
The Potts model plays an essential role in classical statistical mechanics, illustrating many fundamental phenomena. One example is the existence of partially long-range-ordered states, in which some degrees of freedom remain disordered.…