Related papers: Uniqueness for the 3-State Antiferromagnetic Potts…
A phenomenological approach to the ferromagnetic two dimensional Potts model on square lattice is proposed. Our goal is to present a simple functional form that obeys the known properties possessed by the free energy of the q-state Potts…
The paper concerns the $q$-state Potts model (i.e., with spin values in $\{1,\dots,q\}$) on a Cayley tree $\mathbb{T}^k$ of degree $k\geq 2$ (i.e., with $k+1$ edges emanating from each vertex) in an external (possibly random) field. We…
The q-state Potts field theory describes the universality class associated to the spontaneous breaking of the permutation symmetry of q colors. In two dimensions it is defined up to q=4 and exhibits duality and integrability away from…
We solve the antiferromagnetic transition for the Q-state Potts model (defined geometrically for Q generic) on the square lattice. The solution is based on a detailed analysis of the Bethe ansatz equations (which involve staggered source…
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 study the q-state Potts model on the simple cubic lattice with ferromagnetic interactions in one lattice direction, and antiferromagnetic interactions in the two other directions. As the temperature T decreases, the system undergoes a…
In this paper we study a continuum version of the Potts model. Particles are points in R^d, with a spin which may take S possible values, S being at least 3. Particles with different spins repel each other via a Kac pair potential. In mean…
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 performance of Markov chains for the $q$-state ferromagnetic Potts model on random regular graphs. It is conjectured that their performance is dictated by metastability phenomena, i.e., the presence of "phases" (clusters) in…
We consider the Ising model on a general tree under various boundary conditions: all plus, free and spin-glass. In each case, we determine when the root is influenced by the boundary values in the limit as the boundary recedes to infinity.…
We study the antiferromagnetic 3-state Potts model on general (periodic) plane quadrangulations $\Gamma$. Any quadrangulation can be built from a dual pair $(G,G^*)$. Based on the duality properties of $G$, we propose a new criterion to…
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…
Fixing $\beta \ge 0$ and an integer $q \ge 2$, consider the ferromagnetic $q$-Potts measures $\mu_n^{\beta,B}$ on finite graphs ${\sf G}_n$ on $n$ vertices, with external field strength $B \ge 0$ and the corresponding random cluster…
We show that the Wang-Swendsen-Koteck\'y algorithm for antiferromagnetic $q$-state Potts models is nonergodic at zero temperature for $q=3$ on periodic $3m \times 3n$ lattices where $m,n$ are relatively prime. For $q \ge 4$ and/or other…
The q-state ferromagnetic Potts model under a non-zero magnetic field coupled with the 0^th Potts state was investigated by an exact real-space renormalization group approach. The model was defined on a family of diamond hierarchical…
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 study the phase diagram of the triangular-lattice $Q$-state Potts model in the real $(Q,v)$-plane, where $v=e^J-1$ is the temperature variable. Our first goal is to provide an obviously missing feature of this diagram: the position of…
We show that for all sufficiently large d, the uniform proper 3-coloring model (in physics called the 3-state antiferromagnetic Potts model at zero temperature) on Z^d admits multiple maximal-entropy Gibbs measures. This is a consequence of…
It is known rigorously that the phase transition of the $q$-state ferromagnetic Potts model on the square lattice is second order for $q=4$. Despite this fact, some observables of the $q=4$ model show features of a first-order phase…
OpenAI's reasoning model o3-mini-high was used to carry out an exact analytic study of onedimensional ferrimagnetic site- and bond-decorated q-state Potts models. We demonstrate that the finitetemperature ultranarrow phase crossover (UNPC),…