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We establish phase transitions for classes of continuum Delaunay multi-type particle systems (continuum Potts models) with infinite range repulsive interaction between particles of different type. In one class of the Delaunay Potts models…
Diluted mean-field models are graphical models in which the geometry of interactions is determined by a sparse random graph or hypergraph. Based on a nonrigorous but analytic approach called the "cavity method", physicists have predicted…
Temperature inversion due to velocity filtration, a mechanism originally proposed to explain the heating of the solar corona, is demonstrated to occur also in a simple paradigmatic model with long-range interactions, the Hamiltonian…
We have recently proposed a theoretical model for superconductors endowed with two distinct superconducting phases, described by two scalar order parameters which condensate at different critical temperatures. On analyzing the magnetic…
The ground state of the bilayer Kitaev model with the Heisenberg-type interlayer exchange interaction is investigated by means of the exact diagonalization. Calculating the ground-state energy, local quantity defined on each plaquette, and…
The simplified model of first-order transition in a media with frozen long-range transition-temperature disorder is considered. It exhibits the smearing of the transition due to appearance of the intermediate inhomogeneous phase with…
The thermodynamic properties of a one-dimensional model describing spin dynamics in the presence of a twofold orbital degeneracy are studied numerically using the transfer-matrix renormalization group (TMRG). The model contains an…
We consider the long-range random field Ising model in dimension $d = 1, 2$, whereas the long-range interaction is of the form $J_{xy} = |x-y|^{-\alpha}$ with $1< \alpha < 3/2$ for $d=1$ and with $2 < \alpha \leq 3$ for $d = 2$. Our main…
We study the phase transition of the $\pm J$ Heisenberg model in three dimensions. Using a dynamical simulation method that removes a drift of the system, the existence of the spin-glass (SG) phase at low temperatures is suggested. The…
(abridged) In this paper, we present the issues we consider as essential as far as the statistical mechanics of finite systems is concerned. In particular, we emphasis our present understanding of phase transitions in the framework of…
We study phase transitions in models of opinion formation which are based on the social impact theory. Two different models are discussed: (i) a cellular--automata based model of a finite group with a strong leader where persons can change…
From general arguments, that are valid for spin models with sufficiently short-range interactions, we derive strong constraints on the excitation spectrum across a continuous phase transition at zero temperature between a magnetic and a…
We study first order phase transitions that occur when the temperature of the system increases and we identify the conditions that lead to super-heating, a phase where the system can heat up arbitrarily. First order phase transitions with…
The aim of this paper is to illustrate that generalized two-dimensional XY models (proposed by Romano and Zagrebnov) may also support a first-order phase transition. Two approaches are employed to accurately determine the critical parameter…
Fathoming deconfined phases is one of the key issues in modern condensed matter. Striking many-body effects including massive quantum entanglement and coherence may be realized as manifested in quantum spin liquids and topological orders.…
The relation between collective modes and the phase transition in low density nuclear matter is examined. The dispersion relations for collective modes in a linear approach are evaluated within a Landau-Fermi liquid scheme by assuming…
A pure Yang-Mills theory extended by addition of a quartic term is considered in order to study the transition from the quantum tunneling regime to that of classical, i.e. thermal, behaviour. The periodic field configurations are found,…
We analyze the effect of heavy fundamentally charged particles on the finite temperature deconfining phase transition in the 2+1 dimensional Georgi-Glashow model. We show that in the presence of fundamental matter the transition turns into…
Following Fr\"ohlich and Spencer, we study one dimensional Ising spin systems with ferromagnetic, long range interactions which decay as $|x-y|^{-2+\alpha}$, $0\leq \alpha\leq 1/2$. We introduce a geometric description of the spin…
DNA denaturation, wetting in two dimensions, depinning of a flux line, and other problems map onto a phase transition with effective long range interaction. It yields giant non-universal critical indexes, arbitrarily large macroscopic…