Related papers: Potts Models with (17) Invisible States on Thin Gr…
We introduce a non-linear variant of the voter model, the q-voter model, in which q neighbors (with possible repetition) are consulted for a voter to change opinion. If the q neighbors agree, the voter takes their opinion; if they do not…
We consider the two-dimensional random bond $q$-state Potts model within the recently introduced exact framework of scale invariant scattering, exhibit the line of stable fixed points induced by disorder for arbitrarily large values of $q$,…
The quantum $5$-state Potts model is known to possess a perturbative description using complex conformal field theory (CCFT), the analytic continuation of ``theory space" to a complex plane. To study the corresponding complex fixed point on…
In this survey, we give a friendly introduction from a graph theory perspective to the q-state Potts model, an important statistical mechanics tool for analyzing complex systems in which nearest neighbor interactions determine the aggregate…
We use two-dimensional Poissonian random lattices of Voronoi/ Delaunay type to study the effect of quenched coordination number randomness on the nature of the phase transition in the eight-state Potts model, which is of first order on…
We propose a method to identify the order of a Quantum Phase Transition by using area measures of the ground state in phase space. We illustrate our proposal by analyzing the well known example of the Quantum Cusp, and four different…
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…
The q-state Potts model can be formulated in geometric terms, with Fortuin-Kasteleyn (FK) clusters as fundamental objects. If the phase transition of the model is second order, it can be equivalently described as a percolation transition of…
We analyse in depth an $S_3$-invariant nearest-neighbor quantum chain in the region of a U(1)-invariant self-dual multicritical point. We find four distinct proximate gapped phases. One has three-state Potts order, corresponding to…
In this paper, we explore the metastable behavior of the Glauber dynamics associated with the three-state Potts model with an asymmetrical external field at a low-temperature regime. The model exhibits three monochromatic configurations: a…
The q-state Potts model in two dimensions exhibits a first-order transition for q>4. As q->4+ the correlation length at this transition diverges. We argue that this limit defines a massive integrable quantum field theory whose lowest…
We consider the number and distribution of minima in random landscapes defined on non-Euclidean lattices. Using an ensemble where random landscapes are reweighted by a fugacity factor $z$ for each minimum they contain, we construct first a…
We consider the ferromagnetic $q$-state Potts model with zero external field in a finite volume and assume that the stochastic evolution of this system is described by a Glauber-type dynamics parametrized by the inverse temperature $\beta$.…
The investigation of the first-order quantum phase transition (QPT) is far from clarity in comparison to that of the second-order or continuous QPT, in which the order parameter and associated broken symmetry can be clearly identified and…
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…
We consider the two-dimensional dilute q-state Potts model on its first order phase transition surface for 0<q\leq 4. After determining the exact scattering theory which describes the scaling limit, we compute the two-kink form factors of…
As is known, at the Gibbs-Boltzmann equilibrium, the mean-field $q$-state Potts model with a ferromagnetic coupling has only a first order phase transition when $q\geq 3$, while there is no phase transition for an antiferromagnetic…
We define an entropy for a quantum field theory by combining quantum fluctuations, scaling and the maximum entropy concept. This entropy has different behavior in asymptotically free and non--asymptotically free theories. We find that the…
I review some numerical ways to determine the parameters of systems close to a first order phase transition point: energy and specific heat of the coexisting phases and interface tension. Numerical examples are given for the 2-d $q$ states…
We consider a variety of nearest-neighbor spin models defined on the d-dimensional hypercubic lattice Z^d. Our essential assumption is that these models satisfy the condition of reflection positivity. We prove that whenever the associated…