Related papers: Three-point connectivity constant for $q$-state Po…
This paper studies the critical and near-critical regimes of the planar random-cluster model on $\mathbb Z^2$ with cluster-weight $q\in[1,4]$ using novel coupling techniques. More precisely, we derive the scaling relations between the…
We consider critical site percolation on the triangular lattice in the upper half-plane. Let $u_1, u_2$ be two sites on the boundary and $w$ a site in the interior of the half-plane. It was predicted by Simmons, Kleban and Ziff in a paper…
We present results of a numerical simulation of the $q$-state random bond Potts model in two dimensions and for large $q$. In particular, care is taken to study the crossover from the pure model to the random model, as well as the crossover…
We study conditioned random-cluster measures with edge-parameter p and cluster-weighting factor q satisfying q \ge 1. The conditioning corresponds to mixed boundary conditions for a spin model. Interfaces may be defined in the sense of…
A closed-form exact analytical solution for the q-state Potts model on a ladder 2 x oo with arbitrary two-, three-, and four-site interactions in a unit cell is presented. Using the obtained solution it is shown that the finite-size…
We revisit the 3-states Potts model on random planar triangulations as a Hermitian matrix model. As a novelty, we obtain an algebraic curve which encodes the partition function on the disc with both fixed and mixed spin boundary conditions.…
We report numerical estimates of correlation lengths in 2D Potts models from the asymptotic decay of the cluster-diameter distribution. Using this observable we are able to verify theoretical predictions for the correlation length in the…
We solve exactly a special case of the anisotropic directed bond percolation problem in three dimensions, in which the occupation probability is 1 along two spatial directions, by mapping it to a five-vertex model. We determine the…
We establish explicit duality transformations for systems of M q-state Potts models coupled through their local energy density, generalising known results for M=1,2,3. The M-dimensional space of coupling constants contains a selfdual…
The Potts model is one of the most popular spin models of statistical physics. The prevailing majority of work done so far corresponds to the lattice version of the model. However, many natural or man-made systems are much better described…
We perform Monte Carlo simulations of 2-d dynamically triangulated surfaces coupled to Ising and three--states Potts model matter. By measuring spin-spin correlation functions as a function of the geodesic distance we provide substantial…
Using a recently developed method to simulate percolation on large clusters of distributed machines [N. R. Moloney and G. Pruessner, Phys. Rev. E 67, 037701 (2003)], we have numerically calculated crossing, spanning and wrapping…
We analyse in this article the critical behavior of $M$ $q_1$-state Potts models coupled to $N$ $q_2$-state Potts models ($q_1,q_2\in [2..4]$) with and without disorder. The technics we use are based on perturbed conformal theories.…
Using derivatives of primary fields (null or not) with respect to the conformal dimension, we build infinite families of non-trivial logarithmic representations of the conformal algebra at generic central charge, with Jordan blocks of…
We analyze the properly normalized three-point correlator of two protected scalar operators and one higher spin twist-two operator in N=4 super Yang-Mills, in the limit of large spin j. The relevant structure constant can be extracted from…
We study the critical behavior of the 3-state Potts model, where the spins are located at the centers of the occupied squares of the deterministic Sierpinski carpet. A finite-size scaling analysis is performed from Monte Carlo simulations,…
We present a microcanonical Monte Carlo simulation of the site-diluted Potts model in three dimensions with eight internal states, partly carried out in the citizen supercomputer Ibercivis. Upon dilution, the pure model's first-order…
We analyze Monte Carlo simulation and series-expansion data for the susceptibility of the three-state Potts model in the critical region. The amplitudes of the susceptibility on the high- and the low-temperature sides of the critical point…
A new algorithm is presented, which allows to calculate numerically the partition function Z_q of the d-dimensional q-state Potts models for arbitrary real values q>0 at any given temperature T with high precision. The basic idea is to…
We have studied spin-spin correlation functions in the ordered phase of the two-dimensional $q$-state Potts model with $q=10$, 15, and 20 at the first-order transition point $\beta_t$. Through extensive Monte Carlo simulations we obtain…