Related papers: The Potts and random-cluster models
We study the complexity of approximating the partition function of the $q$-state Potts model and the closely related Tutte polynomial for complex values of the underlying parameters. Apart from the classical connections with quantum…
We consider the two dimensional $Q-$ random-cluster Potts model on the torus and at the critical point. We study the probability for two points to be connected by a cluster for general values of $Q\in [1,4]$. Using a Conformal Field Theory…
A random network model which allows for tunable, quite general forms of clustering, degree correlation and degree distribution is defined. The model is an extension of the configuration model, in which stubs (half-edges) are paired to form…
We propose a new effective cluster algorithm of tuning the critical point automatically, which is an extended version of Swendsen-Wang algorithm. We change the probability of connecting spins of the same type, $p = 1 - e^{- J/ k_BT}$, in…
The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset…
In this paper we retrace the recent history of statistics by analyzing all the papers published in five prestigious statistical journals since 1970, namely: Annals of Statistics, Biometrika, Journal of the American Statistical Association,…
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 $1\le q\le 4$…
In 1961 Herbert Simon and Albert Ando published the theory behind the long-term behavior of a dynamical system that can be described by a nearly uncoupled matrix. Over the past fifty years this theory has been used in a variety of contexts,…
We combinatorially prove a new recurrence between the Tutte polynomials of graphs obtained by contraction of the complete graphs $K_{n}$%. This generalizes, to two variables, a relation previously obtained by the author between the…
The cluster algorithm in the fully frustrated Ising model on the square lattice is essentially different from the ones used in other systems. Thus its better understanding is particularly important for finding new lines of development.…
We report on single-cluster Monte Carlo simulations of the Ising, 4-state Potts and 10-state Potts models on quenched ensembles of planar, tri-valent random graphs. We confirm that the first-order phase transition of the 10-state Potts…
This paper deals with the location of the complex zeros of the Tutte polynomial for a class of self-dual graphs. For this class of graphs, as the form of the eigenvalues is known, the regions of the complex plane can be focused on the sets…
We prove an inequality on decision trees on monotonic measures which generalizes the OSSS inequality on product spaces. As an application, we use this inequality to prove a number of new results on lattice spin models and their…
An agglomerative clustering of random variables is proposed, where clusters of random variables sharing the maximum amount of multivariate mutual information are merged successively to form larger clusters. Compared to the previous…
To highlight certain similarities in combinatorial representations of several well known two-dimensional models of statistical mechanics, we introduce and study a new family of models which specializes to these cases after a proper tuning…
Using Monte Carlo simulations in the frame of stochastic series expansion (SSE), we study the three-state quantum Potts model. The cluster algorithm we used is a direct generalization of that for the quantum Ising model. The simulations…
We apply ideas from the cluster method to q-count the permutations of a multiset according to the number of occurrences of certain generalized patterns, as defined by Babson and Steingrimsson. In particular, we consider those patterns with…
We consider a preferential growth model where particles are added one by one to the system consisting of clusters of particles. A new particle can either form a new cluster (with probability q) or join an already existing cluster with a…
We follow the example of Tutte in his construction of the dichromate of a graph (that is, the Tutte polynomial) as a unification of the chromatic polynomial and the flow polynomial in order to construct a new polynomial invariant of maps…
Shift and stretch invariance lead to the exponential-Boltzmann probability distribution. Rotational invariance generates the Gaussian distribution. Particular scaling relations transform the canonical exponential and Gaussian patterns into…