Related papers: Correlation inequalities for the Potts model
In this paper, correlation inequalities which have been considered on Ising model are extended to q-Potts model. It is considered on generalized Potts model with interaction of any number of spins. We replace the set of spin values…
This work is concerned with the theory of Graphical Representation for the Ising and Potts Models over general lattices with non-translation invariant external field. We explicitly describe in terms of the Random Cluster Representation the…
Correlation inequalities have played an essential role in the analysis of ferromagnetic models but have not been established in spin glass models. In this study, we obtain some correlation inequalities for the Ising models with quenched…
The Fortuin-Kasteleyn-Ginibre (FKG) inequality is an invaluable tool in monotone spin systems satisfying the FKG lattice condition, which provides positive correlations for all coordinate-wise increasing functions of spins. This inequality…
For the two-dimensional Q-state Potts model at criticality, we consider Fortuin-Kasteleyn and spin clusters and study the average number N_Gamma of clusters that intersect a given contour Gamma. To leading order, N_Gamma is proportional to…
The two-dimensional Potts model can be studied either in terms of the original Q-component spins, or in the geometrical reformulation via Fortuin-Kasteleyn (FK) clusters. While the FK representation makes sense for arbitrary real values of…
We formulate measures of spin ordering in the $q$-state ferromagnetic Potts model in a generalized external magnetic field that favors or disfavors spin values in a subset $I_s = \{1,...,s\}$ of the total set of $q$ values. The results are…
We discuss a new class of identities between correlation functions which arise from a local Z_2 invariance of the partition function of the q-state Potts model on general graphs or lattices. Their common feature is to relate the thermal…
The percolation of Potts spins with equal values in Potts model on graphs (networks) is considered. The general method for finding the Potts clusters size distributions is developed. It allows for full description of percolation transition…
We present measurements of the fractal dimensions associated to the geometrical clusters for Z_4 and Z_5 spin models. We also attempted to measure similar fractal dimensions for the generalised Fortuyin Kastelyn (FK) clusters in these…
The Fortuin-Kasteleyn (FK) random cluster model, which can be exactly mapped from the $q$-state Potts spin model, is a correlated bond percolation model. By extensive Monte Carlo simulations, we study the FK bond representation of the…
On locally tree-like random graphs, we relate the random cluster model with external magnetic fields and $q\geq 2$ to Ising models with vertex-dependent external fields. The fact that one can formulate general random cluster models in terms…
Numerical simulations on the total mass, the numbers of bonds on the hull, external perimeter, singly connected bonds and gates into large fjords of the Fortuin-Kasteleyn clusters for two-dimensional q-state Potts models at criticality are…
In this note, we present several inequalities in the context of pattern containment, utilizing elementary applications of the Fortuin-Kasteleyn-Ginibre (FKG) inequality and Shearer's lemma.
Topological properties of Fortuin-Kasteleyn clusters are studied on the torus. Namely, the probability that their topology yields a given subgroup of the first homology group of the torus is computed for Q=1, 2, 3 and 4. The expressions…
We revisit in this paper the problem of connectivity correlations in the Fortuin-Kasteleyn cluster representation of the two-dimensional $Q$-state Potts model conformal field theory. In a recent work [M. Picco, S. Ribault and R.…
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…
We prove Griffiths inequalities for the $O(N)$-spin model with inhomogeneous coupling constants and external magnetic field for any $N\geq 2$. This is achieved by using a representation of $O(N)$-spins in terms of random paths that reduces…
In the realm of Boltzmann-Gibbs statistical mechanics there are three well known isomorphic connections with random geometry, namely (i) the Kasteleyn-Fortuin theorem which connects the $\lambda \to 1$ limit of the $\lambda$-state Potts…
In this paper we prove several inequalities by means of diagrammatic expansions, a technique already used in [BG13]. This time we show that iterations of the folding of a probability leads to the proof of some in- equalities by means of a…