Related papers: Four-point boundary connectivities in critical two…
We prove a long-standing conjecture on random-cluster models, namely that the critical point for such models with parameter $q\geq1$ on the square lattice is equal to the self-dual point $p_{sd}(q) = \sqrt q /(1+\sqrt q)$. This gives a…
We study structural properties of the q-color Potts field theory which, for real values of q, describes the scaling limit of the random cluster model. We show that the number of independent n-point Potts spin correlators coincides with that…
Based on conformal symmetry we propose an exact formula for the four-point connectivities of FK clusters in the critical Ising model when the four points are anchored to the boundary. The explicit solution we found displays logarithmic…
We present a Monte Carlo study of various universal amplitude ratios of the two dimensional q=4 Potts model. We simulated the model close to criticality in both phases taking care to keep the systematic errors, due to finite size effects…
In this paper, we prove that the large scale properties of a number of two-dimensional lattice models are rotationally invariant. More precisely, we prove that the random-cluster model on the square lattice with cluster-weight $1\le q\le 4$…
Universality, encompassing critical exponents, scaling functions, and dimensionless quantities, is fundamental to phase transition theory. In finite systems, universal behaviors are also expected to emerge at the pseudocritical point.…
The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By…
We derive the boundary four-point Green's functions for conformal loop ensembles (CLE) with $\kappa\in(4,8)$. Specializing to $\kappa=6$ and $\kappa=16/3$, we establish the exact formulas for the boundary four-point connectivities in…
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…
The rigidity transition occurs when, as the density of microscopic components is increased, a disordered medium becomes able to transmit and ensure macroscopic mechanical stability, owing to the appearance of a space-spanning rigid…
We present a study of connectivity percolation in suspensions of hard spherocylinders by means of Monte Carlo simulation and connectedness percolation theory. We focus attention on polydispersity in the length, the diameter and the…
I consider a one dimensional system of particles which interact through a hard core of diameter $\si$ and can connect to each other if they are closer than a distance $d$. The mean cluster size increases as a function of the density $\rho$…
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 study the number of clusters in two-dimensional (2d) critical percolation, N_Gamma, which intersect a given subset of bonds, Gamma. In the simplest case, when Gamma is a simple closed curve, N_Gamma is related to the entanglement entropy…
We present a numerical study of 2D random-bond Potts ferromagnets. The model is studied both below and above the critical value $Q_c=4$ which discriminates between second and first-order transitions in the pure system. Two geometries are…
We develop a fluctuation theory of connectivities for subcritical random cluster models. The theory is based on a comprehensive nonperturbative probabilistic description of long connected clusters in terms of essentially one-dimensional…
Percolation problems appear in a large variety of different contexts ranging from the design of composite materials to vaccination strategies on community networks. The key observable for many applications is the percolation threshold.…
Based on the spectrum identified in our earlier work [arXiv:1809.02191], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the $Q$-state Potts model. Crucial in our…
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…
A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…