Related papers: Large deviations and a phase transition in the Blo…
We consider the problem associated to recovering the block structure of an Ising model given independent observations on the binary hypercube. This new model, called the Ising blockmodel, is a perturbation of the mean field approximation of…
We study a bottleneck spin model with $N$ spins, split into two Curie-Weiss models at low temperature with a bottleneck between them. We propose multiple ways of how to realize such a bottleneck and study its influence on the phase…
We consider magnetic friction between two systems of $q$-state Potts spins which are moving along their boundaries with a relative constant velocity $v$. Due to the interaction between the surface spins there is a permanent energy flow and…
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…
A combinatorial approach is used to study the critical behavior of a $q$-state Potts model with a round-the-face interaction. Using this approach it is shown that the model exhibits a first order transition for $q>3$. A second order…
The basic $\kappa$-color box-ball (BBS) system is an integrable cellular automaton on one dimensional lattice whose local states take $\{0,1,\cdots,\kappa \}$ with $0$ regarded as an empty box. The time evolution is defined by a…
We define a block observable for the $q$-state Potts model which exhibits an intermittent behaviour at the critical point. We express the intermittency indices of the normalised moments in terms of the magnetic critical exponent $\beta…
We study the limiting spectral distribution of sample covariance matrices $XX^T$, where $X$ are $p\times n$ random matrices with correlated entries, for the cases $p/n\to y\in [0,\infty)$. If $y>0$, we obtain the Mar\v{c}enko-Pastur…
We derive the exact actions of the $Q$-state Potts model valid on any graph, first for the spin degrees of freedom, and second for the Fortuin-Kasteleyn clusters. In both cases the field is a traceless $Q$-component scalar field…
In this paper we study a continuum version of the Potts model. Particles are points in R^d, with a spin which may take S possible values, S being at least 3. Particles with different spins repel each other via a Kac pair potential. In mean…
Using the theory of large deviations, we analyze the phase transition structure of the Curie-Weiss-Potts spin model, which is a mean-field approximation to the Potts model. This analysis is carried out both for the canonical ensemble and…
A system of interacting multiclass finite-state jump processes is analyzed. The model under consideration consists of a block-structured network with dynamically changing multi-colors nodes. The interaction is local and described through…
In this thesis, we present results from the investigation of two problems, one related to the phase transition of long-range Ising models and the other one associated with the characterization of equilibrium states in quantum spin systems.…
For $\Delta \ge 5$ and $q$ large as a function of $\Delta$, we give a detailed picture of the phase transition of the random cluster model on random $\Delta$-regular graphs. In particular, we determine the limiting distribution of the…
It is an important topic to investigate nature of the phase transition in wide area of science such as statistical physics, materials science, and computational science. Recently it has been reported the efficiency of quantum adiabatic…
We study the metastable equilibrium properties of the Potts model with heat-bath transition rates using a novel expansion. The method is especially powerful for large number of state spin variables and it is notably accurate in a rather…
This is the second of two papers on a continuum version of the Potts model, where particles are points in $\mathbb R^d$, $d\ge 2$, with a spin which may take $S\ge 3$ possible values. Particles with different spins repel each other via a…
We present extensive numerical simulations of a family of non-equilibrium Potts models with absorbing states that allows for a variety of scenarios, depending on the number of spin states and the range of the spin-spin interactions. These…
We prove that random-cluster models with q larger than 1 on a variety of planar lattices have a sharp phase transition, that is that there exists some parameter p_c below which the model exhibits exponential decay and above which there…
The behaviour of the mean Euler-Poincar\'{e} characteristic and mean Betti's numbers in the Ising model with arbitrary spin on $\mathbbm{Z}^2$ as functions of the temperature is investigated through intensive Monte Carlo simulations. We…