Related papers: Ensemble inequivalence in systems with long-range …
We consider spin systems with long-range interactions in nonadditive regime. When the non-additive scaling limit is employed, the energy and the entropy compete and the system exhibits some phase transitions. Such systems do not satisfy the…
In bulk systems the calculation of the main thermodynamic quantities leads to the same expectation values in the thermodynamic limit, regardless of the choice of the statistical ensemble. Single linear molecules can be still regarded as…
We propose a hybrid model governed by the Blume-Emery-Griffiths (BEG) Hamiltonian with a mean-field-like interaction, where the spins are randomly quenched such that some of them are "pure" Ising and the others admit the BEG set of states.…
The presence of non-local and long-range interactions in quantum systems induces several peculiar features in their equilibrium and out-of-equilibrium behavior. In current experimental platforms control parameters such as interaction range,…
Designing the phase behavior of multicomponent mixtures is a rich area with many potential applications. One key question is how more than $M+1$ phases, as would normally be allowed by Gibbs' phase rule at generic temperature in a mixture…
The grand canonical ensemble lies at the core of quantum and classical statistical mechanics. A small system thermalizes to this ensemble while exchanging heat and particles with a bath. A quantum system may exchange quantities represented…
We investigate the ensemble inequivalence of the spherical spin glass model with nonlinear interactions of polynomial order $p$. This model is solved exactly for arbitrary $p$ and is shown to have first-order phase transitions between the…
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…
We study inequivalence of canonical and microcanonical ensembles in the mean-field Blume-Emery-Griffiths model. This generalizes previous results obtained for the Blume-Capel model. The phase diagram strongly depends on the value of the…
Small thermodynamic systems exhibit peculiar behavior different from that observed in long-scale systems. Non-equilibrium processes taking place in those systems are strongly influenced by the presence of fluctuations which can be large.…
New methods are presented which enables one to analyze the thermodynamics of systems with long-range interactions. Generically, such systems have entropies which are non-extensive, (do not scale with the size of the system). We show how to…
An instructive and apparently simple model of fully-coupled rotators, the so-called Hamiltonian Mean Field (HMF) model, together with a generalized version with variable interaction range, have revealed a very complex out-of-equilibrium…
The dynamics and the thermodynamics of particles/spins interacting via long-range forces display several unusual features with respect to systems with short-range interactions. The Hamiltonian Mean Field (HMF) model, a Hamiltonian system of…
We examine the long-term behaviour of non-integrable, energy-conserved, 1D systems of macroscopic grains interacting via a contact-only generalized Hertz potential and held between stationary walls. Existing dynamical studies showed the…
Long-range interacting systems may exhibit ensemble inequivalence and can possibly attain equilibrium states under completely open conditions, for which energy, volume and number of particles simultaneously fluctuate. Here we consider a…
Mutual equilibrium in long-range interacting systems which involve nonadditive energy, is effectively described in terms of entropy with a nonadditive composition rule. As an example, long range Ising model is considered. The generality of…
The phenomenon of partial equivalence of statistical ensembles is illustrated by discussing two examples, the mean-field XY and the mean-field spherical model. The configurational parts of these systems exhibit partial equivalence of the…
Interacting particle systems are in frequent use to model collective behaviour in various situations and applications. For many systems, the interaction between the agents is restricted to an underlying network structure and often, the…
Realistic effective interparticle interactions of quantum many-body systems are widely seen as being short-range. However, the rigorous mathematical analysis of this type of model turns out to be extremely difficult, in general, with many…
We consider the statistical mechanics of a small gaseous system subject to a constant external field. As is well known, in the canonical ensemble the system i) obeys a barometric formula for the density profile and ii) the kinetic…