Related papers: Critical exponents for planar random-cluster model…
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 this paper we consider random planar maps weighted by the self-dual Fortuin--Kasteleyn model with parameter $q \in (0,4)$. Using a bijection due to Sheffield and a connection to planar Brownian motion in a cone we obtain rigorously the…
We consider the two dimensional $Q-$ random-cluster Potts model on the torus and at the critical point. We study the probability for two points to be connected by a cluster for general values of $Q\in [1,4]$. Using a Conformal Field Theory…
We show that scale invariant scattering theory allows to exactly determine the critical points of two-dimensional systems with coupled $O(N)$ and Ising order pameters. The results are obtained for $N$ continuous and include criticality of…
The critical behavior of the Baxter-Wu model belongs to the universality class of the four-state Potts model. While the introduction of annealed vacancies does not alter the criticality of the four-state Potts model, the dilute Baxter-Wu…
We use scale invariant scattering theory to exactly determine the renormalization group fixed points of a $q$-state Potts model coupled to an $r$-state Potts model in two dimensions. For integer values of $q$ and $r$ the fixed point…
We consider the fractal dimensions of critical clusters occurring in configurations of a q-state Potts model coupled to the planar random graphs of the dynamical triangulations formulation of Euclidean quantum gravity in two dimensions. For…
We consider a critical Fortuin-Kasteleyn (FK) percolation with cluster weight $q \in [1,4)$ in the plane, and color its clusters in red (respectively blue) with probability $r \in (0,1)$ (respectively $1-r$), independently of each other. We…
The self-dual random-bond eight-state Potts model is studied numerically through large-scale Monte Carlo simulations using the Swendsen-Wang cluster flipping algorithm. We compute bulk and surface order parameters and susceptibilities and…
We compute critical properties of a general class of quantum spin chains which are quadratic in the Fermi operators and can be solved exactly under certain symmetry constraints related to the classical compact groups $U(N)$, $O(N)$ and…
We conjecture an exact form for an universal ratio of four-point cluster connectivities in the critical two-dimensional $Q$-color Potts model. We also provide analogous results for the limit $Q\rightarrow 1$ that corresponds to percolation…
The phase diagram and critical behavior of the spin-1 Baxter-Wu model with a crystal field in two dimensions is explored by renormalization group, conventional finite-size scaling and conformal invariance techniques. We found that the phase…
In the mixture modeling frame, this paper presents the polynomial Gaussian cluster-weighted model (CWM). It extends the linear Gaussian CWM, for bivariate data, in a twofold way. Firstly, it allows for possible nonlinear dependencies in the…
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…
By Monte Carlo simulation we study the critical exponents governing the transition of the three-dimensional classical O(4) Heisenberg model, which is considered to be in the same universality class as the finite-temperature QCD with…
The two-dimensional $Q$-state Potts model with real couplings has a first-order transition for $Q>4$. We study a loop-model realization in which $Q$ is a continuous parameter. This model allows for the collision of a critical and a…
We explicitly evaluate the free energy of the random cluster model at its critical point for 0 < q < 4 using an exact result due to Baxter, Temperley and Ashley. It is found that the resulting expression assumes a form which depends on…
We show how to couple two critical Q-state Potts models to yield a new self-dual critical point. We also present strong evidence of a dense critical phase near this critical point when the Potts models are defined in their completely packed…
The $q=2$ random cluster model is studied in the context of two mean field models: The Bethe lattice and the complete graph. For these systems, the critical exponents that are defined in terms of finite clusters have some anomalous values…
We prove that random-cluster models with q larger than 1 on a variety of planar lattices have a sharp phase transition, that is that there exists some parameter p_c below which the model exhibits exponential decay and above which there…