相关论文: Random clusters in the Villain and XY models

In these notes, we discuss a selection of topics on several models of planar statistical mechanics. We consider the Ising, Potts, and more generally abelian spin models; the discrete Gaussian free field; the random cluster model; and the…

The study gives a decisive answer to the recently risen question about the type and origin of interaction between spin vortices and spin vacancies in 2D spin models. The approach is based on the low-temperature approximation of the 2D XY…

The geometrical critical behaviour of the two-dimensional Q-state Potts model is usually studied in terms of the Fortuin-Kasteleyn (FK) clusters, or their surrounding loops. In this paper we study a quite different geometrical object: the…

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…

In the strong coupling limit the partition function of SU(2) gauge theory can be reduced to that of the continuous spin Ising model with nearest neighbour pair-interactions. The random cluster representation of the continuous spin Ising…

An extension of the Ising spin configurations to continuous functions is used for an exact representation of the Random Field Ising Model's order parameter in terms of disagreement percolation. This facilitates an extension of the recent…

To investigate novel aspects of pattern formation in spin systems, we use a mapping between reactive concentrations in a reaction-diffusion system and spin orientations in a dynamic multiple-spin Ising model. While pattern formation in…

We show that a class of spin models, containing the Ashkin-Teller model, admits a generalized random-cluster (GRC) representation. Moreover we show that basic properties of the usual representation, such as FKG inequalities and comparison…

The spontaneous symmetry breaking in the Ising model can be equivalently described in terms of percolation of Wolff clusters. In O(n) spin models similar clusters can be built in a general way, and they are currently used to update these…

Coordination processes in complex systems can be related to the problem of collective ordering in networks, many of which have modular organization. Investigating the order-disorder transition for Ising spins on modular random networks,…

Any limiting point process for the time normalized exceedances of high levels by a stationary sequence is necessarily compound Poisson under appropriate long range dependence conditions. Typically exceedances appear in clusters. The…

We consider the fractal dimensions of critical clusters occurring in configurations of a q-state Potts model coupled to the planar random graphs of the dynamical triangulations formulation of Euclidean quantum gravity in two dimensions. For…

I consider the problem of deriving couplings of a statistical model from measured correlations, a task which generalizes the well-known inverse Ising problem. After reminding that such problem can be mapped on the one of expressing the…

We find the cross-over behavior for the spin-spin correlation function for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation approach of the perturbation series…

We study graphical representations for two related models. The first model is the transverse field quantum Ising model, an extension of the original Ising model which was introduced by Lieb, Schultz and Mattis in the 1960's. The second…

Tiny fluctuations of the Cosmic Microwave Background as well as various observable quantities obtained by spin raising and spin lowering of the effective gravitational lensing potential of distant galaxies and galaxy clusters, are described…

A recent trend in machine learning has been to enrich learned models with the ability to explain their own predictions. The emerging field of Explainable AI (XAI) has so far mainly focused on supervised learning, in particular, deep neural…

In this paper, we investigate temporal clusters of extremes defined as subsequent exceedances of high thresholds in a stationary time series. Two meaningful features of these clusters are the probability distribution of the cluster size and…

A problem of practical significance is the analysis of large, spatially distributed data sets. The problem is more challenging for variables that follow non-Gaussian distributions. We show that the spatial correlations between variables can…

We study the evolution of social clusters, in an analogy with physical spin systems, and in detail show the importance of the concept of the "self" of each agent with quantifiable variable attributes. We investigate the effective influence…