Related papers: Crossing bonds in the random-cluster model

We present results of a numerical simulation of the 3-state Potts model with random bond, in two dimension. In particular, we measure the critical exponent associated to the magnetization and the specific heat. We also compare these…

A crossing probability for the critical four-state Potts model on an $L\times M$ rectangle on a square lattice is numerically studied. The crossing probability here denotes the probability that spin clusters cross from one side of the…

We exploit the identification between the critical theory of the 3-state Potts model and the D_5 conformal model. This allows us to determine all 3-point correlations involving the fields associated with the Potts order parameter and the…

Enormous advances have been made in the past 20 years in our understanding of the random-field Ising model, and there is now consensus on many aspects of its behavior at least in thermal equilibrium. In contrast, little is known about its…

We address the geometrical critical behavior of the two-dimensional Q-state Potts model in terms of the spin clusters (i.e., connected domains where the spin takes a constant value). These clusters are different from the usual…

We propose a matrix-model derivation of the scaling exponents of the critical and tricritical q-states Potts model coupled to gravity on a sphere. In close analogy with the $O(n)$ model, we reduce the determination of the one-loop-to-vacuum…

Analytical results are derived for the bond percolation threshold and the size of the giant connected component in a class of random networks with non-zero clustering. The network's degree distribution and clustering spectrum may be…

The study of crossing probabilities - i.e. probabilities of existence of paths crossing rectangles - has been at the heart of the theory of two-dimensional percolation since its beginning. They may be used to prove a number of results on…

Renormalization group and Coulomb gas mappings are used to derive theoretical predictions for the corrections to the exactly known asymptotic fractal masses of the hull, external perimeter, singly connected bonds and total mass of the…

We introduce an exact replica method for the study of critical systems with quenched bond randomness in two dimensions. For the $q$-state Potts model we show that a line of renormalization group fixed points interpolates from weak to strong…

We first study crossing statistics in random connection models (RCM) built on marked Poisson point processes on $\mathbb R^d$. Under general assumptions, we show exponential tail bounds for the number of crossings of a box contained in the…

We investigate the critical properties of the four-state commutative random permutation glassy Potts model in three and four dimensions by means of Monte Carlo simulation and of a finite size scaling analysis. Thanks to the use of a field…

Percolation, a paradigmatic geometric system in various branches of physical sciences, is known to possess logarithmic factors in its correlators. Starting from its definition, as the $Q\rightarrow1$ limit of the $Q$-state Potts model with…

The critical behavior of three-state statistical models invariant under the full symmetry group $S_3$ and its dependence on space dimension have been a matter of interest and debate. In particular, the phase transition of the 3-state Potts…

The effect of quenched impurities on systems which undergo first-order phase transitions is studied within the framework of the q-state Potts model. For large q a mapping to the random field Ising model is introduced which provides a simple…

We numerically investigate the influence of self-attraction on the critical behaviour of a polymer in two dimensions, by means of an analysis of finite-size results of transfer-matrix calculations. The transfer matrix is constructed on the…

We present study of finite-size scaling and universality of crossing probabilities for the $q$-state Potts model. Crossing probabilities of the Potts model are similar ones in percolation problem. We numerically investigated scaling of…

We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations, using an efficient cluster algorithm and a finite-size scaling analysis. The critical points and four critical exponents of the model…

We consider random q-state Potts models for $3\le q \le 8$ on the square lattice where the ferromagnetic couplings take two values $J_1>J_2$ with equal probabilities. For any q the model exhibits a continuous phase transition both in the…

Critical exponents characterize the divergent scaling of thermodynamic quantities near phase transitions and allow for the classification of physical systems into universality classes. While quantum gases thermalizing by interparticle…