Related papers: The Potts model built on sand
We compare results of the exact field theory of phase separation in two dimensions with Monte Carlo simulations for the $q$-state Potts model with boundary conditions producing an interfacial region separating two pure phases. We confirm in…
For any integers $d,q\ge 3$, we consider the $q$-state ferromagnetic Potts model with an external field on a sequence of expander graphs that converges to the $d$-regular tree $\mathtt{T}_d$ in the Benjamini-Schramm sense. We show that…
I study a dimer model on the square lattice with nearest-neighbor exclusion as the only interaction. Detailed simulations using tomographic entropic sampling show that as the chemical potential is varied, there is a strongly discontinuous…
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 note that it is possible to construct a bond vertex model that displays q-state Potts criticality on an ensemble of phi3 random graphs of arbitrary topology, which we denote as ``thin'' random graphs in contrast to the fat graphs of the…
We define a four-state Potts model ensemble on the square lattice, with the constraints that neighboring spins must have different values, and that no plaquette may contain all four states. The spin configurations may be mapped into those…
Monte Carlo simulations are performed to study the two-dimensional Potts models with q=3 and 4 states on directed Small-World network. The disordered system is simulated applying the Heat bath Monte Carlo update algorithm. A first-order and…
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 study the effect of interfacial phenomena in two-dimensional perfect and random (or disordered) $q$-state Potts models with continuous phase transitions, using, mainly, Monte Carlo techniques. In particular, for the total interfacial…
We consider q-state Potts models coupled by their energy operators. Restricting our study to self-dual couplings, numerical simulations demonstrate the existence of non-trivial fixed points for 2 <= q <= 4. These fixed points were first…
In a recent paper we introduced two Potts-like models in three dimensions, which share the following properties: (A) One of the ice rules is always fulfilled (in particular also at infinite temperature). (B) Both ice rules hold for…
We study the bi-dimensional $q$-Potts model with long-range bond correlated disorder. Similarly to [C. Chatelain, Phys. Rev. E 89, 032105], we implement a disorder bimodal distribution by coupling the Potts model to auxiliary…
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 solve the q-state Potts model with anti-ferromagnetic interactions on large random lattices of finite coordination. Due to the frustration induced by the large loops and to the local tree-like structure of the lattice this model behaves…
We present a proof of the power law decay of magnetic moment for the $q$-state antiferromagnetic Potts model on the regular tree at the critical temperature, and also justify that the exact exponent is $\frac{1}{2}$. Our proof relies on the…
The phase transition in the q-state Potts model with homogeneous ferromagnetic couplings is strongly first order for large q, while is rounded in the presence of quenched disorder. Here we study this phenomenon on different two-dimensional…
The "bootstrap determination" of the geometrical correlation functions in the two-dimensional Potts model proposed in a paper [arXiv:1607.07224] was later shown in [arXiv:1809.02191] to be incorrect, the actual spectrum of the model being…
By computing the low-lying energy excitation spectra with the density matrix renormalization group algorithm we show that boundaries polarized in the direction of the transverse field lead to scale-invariant conformal towers of states at…
We present a simple yet generic model for the behavior of a system of many surface-attached flexible polymers with rigid side chains. Beyond its potential application in describing the dynamics of the extracellular matrix of mammalian…
We study the square-lattice three-state Potts model with the ferromagnetic next-nearest-neighbor coupling at finite temperature. Using the level-spectroscopy method, we numerically analyze the excitation spectrum of the transfer matrices…