Related papers: Backbone three-point correlation function in the t…
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…
We present the results of a Monte Carlo study of the three-dimensional anti-ferromagnetic 3-state Potts model. We compute various cumulants in the neighbourhood of the critical coupling. The comparison of the results with a recent high…
The Potts conformal field theory is an analytic continuation in the central charge of conformal field theory describing the critical two-dimensional $Q$-state Potts model. Four-point functions of the Potts conformal field theory are…
The two-dimensional random-bond Q-state Potts model is studied for Q near 2 via the perturbative renormalisation group to one loop. It is shown that weak disorder induces cross-correlations between the quenched-averages of moments of the…
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…
A Fortuin-Kasteleyn cluster on a torus is said to be of type $\{a,b\}, a,b\in\mathbb Z$, if it possible to draw a curve belonging to the cluster that winds $a$ times around the first cycle of the torus as it winds $-b$ times around the…
We use Monte Carlo simulations to measure the spin-spin correlation function in the disordered phase of two-dimensional $q$-state Potts models with $q=10,15$, and $20$ at the first-order transition point $\beta_t$. To extract the…
The universality of the crossing probability $\pi_{hs}$ of a system to percolate only in the horizontal direction, was investigated numerically by using a cluster Monte-Carlo algorithm for the $q$-state Potts model for $q=2,3,4$ and for…
We propose a new method for the computation of quantum three-point functions for operators in su(2) sectors of N=4 super Yang-Mills theory. The method is based on the existence of a unitary transformation relating inhomogeneous and…
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…
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…
We construct local generalizations of 3-state Potts models with exotic critical points. We analytically show that these are described by non-diagonal modular invariant partition functions of products of $Z_3$ parafermion or $u(1)_6$…
We analyse parafermionic operators in the Q-state Potts model from three different perspectives. First, we explicitly construct lattice holomorphic observables in the Fortuin-Kasteleyn representation, and point out some special simplifying…
A matching algorithm for the identification of backbones in percolation problems is introduced. Using this procedure, percolation backbones are studied in two- to five-dimensional systems containing 1.7x10^7 sites, two orders of magnitude…
The Q-state Potts model can be extended to noninteger and even complex Q in the FK representation. In the FK representation the partition function,Z(Q,a), is a polynomial in Q and v=a-1(a=e^-T) and the coefficients of this…
The scaling limit as T->0 of the antiferromagnetic three-state Potts model on the square lattice is described by the sine-Gordon quantum field theory at a specific value of the coupling. We show that the correspondence follows unambigously…
Field-theoretical calculations predict that, at the upper critical dimension $d_c=4$, the finite-size scaling (FSS) behaviors of the Ising model would be modified by multiplicative logarithmic corrections with thermal and magnetic…
We perform Monte Carlo simulations using the Wolff cluster algorithm of {\it multiple} $q=2,3,4$ state Potts models on dynamical phi-cubed graphs of spherical topology in order to investigate the $c>1$ region of two-dimensional quantum…
Generalizing the mapping between the Potts model with nearest neighbor interaction and six vertex model, we build a family of "fused Potts models" related to the spin $k/2$ ${\rm U}_{q}{\rm su}(2)$ invariant vertex model and quantum spin…
This paper presents a comparison of the predictions for the 2 and 3-point correlation functions of density fluctuations, xi_2 and xi_3, in gravitational perturbation theory (PT) against large Cold Dark Matter (CDM) simulations. This…