Related papers: Potts Partition Function Zeros and Ground State En…
We present the exact solution of the 1D classical short-range Potts model with invisible states. Besides the $q$ states of the ordinary Potts model, this possesses $r$ additional states which contribute to the entropy, but not to the…
We explore connections between the phenomenon of correlation decay and the location of Lee-Yang and Fisher zeros for various spin systems. In particular we show that, in many instances, proofs showing that weak spatial mixing on the Bethe…
We study the 3-state hexagonal-lattice Potts antiferromagnet by a Monte Carlo simulation using the Wang-Swendsen-Kotecky cluster algorithm. We study the staggered susceptibility and the correlation length, and we confirm that this model is…
We study the critical behavior of the q-state Potts model with random ferromagnetic couplings. Working with the cluster representation the partition sum of the model in the large-q limit is dominated by a single graph, the fractal…
We investigate the convergence properties of finite-temperature perturbation theory by considering the mathematical structure of thermodynamic potentials using complex analysis. We discover that zeros of the partition function lead to poles…
The critical phenomena of two-dimensional (2D) antiferromagnetic $q$-state Potts model on the square lattice with $q=2,3,4,5$ and 6 are investigated using the technique of supervised neural network (NN). Unlike the conventional NN…
In this paper we study the phase diagram of the five-state Potts antiferromagnet on the bisected-hexagonal lattice. This question is important since Delfino and Tartaglia recently showed that a second-order transition in a five-state Potts…
We study the chromatic polynomials for m \times n square-lattice strips, of width 9 <= m <= 13 (with periodic boundary conditions) and arbitrary length n (with free boundary conditions). We have used a transfer matrix approach that allowed…
We derive a universal relation for the critical temperatures of the $q$-state Potts model based on the counting of domain-wall microstates. By balancing interface energy against configurational entropy, we show that the critical temperature…
We use the partition functions on S^1 x S^n of various conformal field theories in four and six dimensions in the limit of vanishing coupling to study the high temperature thermodynamics. Certain modular properties exhibited by the…
We investigate the 2- and 3-state ferromagnetic Potts models on the simple cubic lattice using the tensor renormalization group method with higher-order singular value decomposition (HOTRG). HOTRG works in the thermodynamic limit, where we…
We establish two expansions of the Potts model partition function of a graph. One is along the deletions of a graph, a rewritten formula given in Biggs (1977). The other is along the contractions of a graph. Then, we specialize the…
In 1993, Baxter gave $2^{m_Q}$ eigenvalues of the transfer matrix of the $N$-state superintegrable chiral Potts model with spin-translation quantum number $Q$, where $m_Q=\lfloor(NL-L-Q)/N\rfloor$. In our previous paper we studied the Q=0…
We prove that the polynomials generated by the relation $\displaystyle{\sum_{m=0}^{\infty} H_m(z)t^m=\frac{1}{P(t)+z t^r Q(t)}}$ are hyperbolic for $m \gg 1$ given that the zeros of the real polynomials $P$ and $Q$ are real and sufficiently…
We study the three-state antiferromagnetic Potts model on the simple-cubic lattice, paying attention to the surface critical behaviors. When the nearest neighboring interactions of the surface is tuned, we obtain a phase diagram similar to…
We consider the problem of sampling from the Potts model on random regular graphs. It is conjectured that sampling is possible when the temperature of the model is in the uniqueness regime of the regular tree, but positive algorithmic…
We study the partition function Z_{G(nk,k)}(Q,v) of the Q-state Potts model on the family of (non-planar) generalized Petersen graphs G(nk,k). We study its zeros in the plane (Q,v) for 1<= k <= 7. We also consider two specializations of…
We prove several theorems concerning Tutte polynomials $T(G,x,y)$ for recursive families of graphs. In addition to its interest in mathematics, the Tutte polynomial is equivalent to an important function in statistical physics, the Potts…
We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically,…
We provide evidence that it is computationally difficult to approximate the partition function of the ferromagnetic q-state Potts model when q>2. Specifically we show that the partition function is hard for the complexity class #RHPi_1…