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Phase transition in the two-dimensional $q$-state Potts model with random ferromagnetic couplings in the large-q limit is conjectured to be described by the isotropic version of the infinite randomness fixed point of the random…
An exact analytical solution of the statistical multifragmentation model is found in thermodynamic limit. The model exhibits a 1-st order phase transition of the liquid-gas type. The mixed phase region of the phase diagram, where the gas of…
This paper presents an in-depth analysis of the anatomy of both thermodynamics and statistical mechanics, together with the relationships between their constituent parts. Based on this analysis, using the renormalization group and…
Microcanonical statistics can be well applied to non-extensive systems like nuclei, atomic clusters and systems at phase transitions of first order with inhomogeneous configurations like phase separation. No thermodynamic limit has to be…
The relation between thermodynamic phase transitions in classical systems and topology changes in their state space is discussed for systems in which equivalence of statistical ensembles does not hold. As an example, the spherical model…
Due to the equivalence of the statistical ensembles thermostatic properties of physical systems with short-range interactions can be calculated in different ensembles leading to the same physics. In particular, the ensemble equivalence…
The two-dimensional (2D) random-bond Ising model has a novel multicritical point on the ferromagnetic to paramagnetic phase boundary. This random phase transition is one of the simplest examples of a 2D critical point occurring at both…
(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…
The postulational basis of classical thermodynamics has been expanded to incorporate equilibrium fluctuations. The main additional elements of the proposed thermodynamic theory are the concept of quasi-equilibrium states, a definition of…
Random matrix models provide a phenomenological description of a vast variety of physical phenomena. Prominent examples include the eigenvalue statistics of quantum (chaotic) systems, which are conveniently characterized using the spectral…
We consider a family of potentials f, derived from the Hofbauer potentials, on the symbolic space Omega=\{0,1\}^\mathbb{N} and the shift mapping $\sigma$ acting on it. A Ruelle operator framework is employed to show there is a phase…
We develop a model in the framework of nuclear fragmentation at thermodynamic equilibrium which can be mapped onto an Ising model with constant magnetization. We work out the thermodynamic properties of the model as well as the properties…
The thermodynamic limit in statistical thermodynamics of many-particle systems is an important but often overlooked issue in the various applied studies of condensed matter physics. To settle this issue, we review tersely the past and…
The thermodynamic limit of the internal energy and the entropy of the system of quantum interacting particles in random medium is shown to exist under the crucial requirements of stability and temperedness of interactions. The energy turns…
Investigation on foundational aspects of quantum statistical mechanics recently entered a renaissance period due to novel intuitions from quantum information theory and to increasing attention on the dynamical aspects of single quantum…
We discuss the status of thermal model descriptions of particle ratios in central nucleus-nucleus collisions at ultra-relativistic energy. An alternative to the ``Cleymans-Redlich'' interpretation of the freeze-out trajectory is given in…
The relationship between thermodynamics and statistical physics is valid in the thermodynamic limit - when the number of particles becomes very large. Here, we study thermodynamics in the opposite regime - at both the nano scale, and when…
In this paper we give a complete analysis of the phase transitions in the mean-field Blume-Emery-Griffiths lattice-spin model with respect to the canonical ensemble, showing both a second-order, continuous phase transition and a…
In this paper we give a complete analysis of the phase transitions in the mean-field Blume-Emery-Griffiths lattice-spin model with respect to the canonical ensemble, showing both a second-order, continuous phase transition and a…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…