Ensemble nonequivalence in random graphs with modular structure
Breaking of equivalence between the microcanonical ensemble and the canonical ensemble, describing a large system subject to hard and soft constraints, respectively, was recently shown to occur in…
Ensemble inequivalence and absence of quasi-stationary states in long-range random networks
Ensemble inequivalence has been previously displayed only for long-range interacting systems with non-extensive energy. In order to perform the thermodynamic limit, such systems require an…
Ensemble equivalence in spin systems with short-range interactions
We study the problem of ensemble equivalence in spin systems with short-range interactions under the existence of a first-order phase transition. The spherical model with nonlinear nearest-neighbour…
Complete analysis of ensemble inequivalence in the Blume-Emery-Griffiths model.
- PhysicsPhysical review. E
Ergodicity breaking is discussed, which is highlighted by the presence of gaps in the accessible values of magnetization at low energies: it also displays new interesting patterns that are not present in the Blume-Capel model.
Long-range Interactions and Diluted Networks
Long-range interactions appear in gravitational and Coulomb systems, two-dimensional hydrodynamics, plasmas, etc. These physical systems are studied by a variety of theoretical and numerical methods,…
Metastability and discrete spectrum of long-range systems
- PhysicsProceedings of the National Academy of Sciences
The spectrum of systems with power-law decaying couplings remains discrete up to the thermodynamic limit, showing that several traditional results on the chaotic nature of the spectrum in many-body quantum systems are not satisfied in the presence of long-range interactions.
Statistical mechanics: contributions to rigidity percolation and long range interacting systems
The statistical mechanics of long range interacting systems was already the subject of my PhD thesis, done under the joint supervision of Thierry Dauxois and Stefano Ruffo, but research on the subject has followed new directions since 2003.
The ambiguity of nestedness under soft and hard constraints
- Computer ScienceScientific reports
This work proposes a clarification that exploits the recent finding that random networks where the degrees are enforced as hard constraints (microcanonical ensembles) are thermodynamically different from random networksWhere the degrees is enforced as soft constraints (canonicalEnsembles), and disentangles distinct notions of nestedness captured by different metrics.
Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons
In this review we recapitulate the basic features of the flat-band spin systems and briefly summarize earlier studies in the field. Main emphasis is made on recent developments which include results…
SHOWING 1-10 OF 24 REFERENCES
The cavity method for large deviations
- Computer Science
The approach, based on an extension of the cavity method to atypical realizations of the quenched disorder, allows us to compute exponentially small probabilities (rate functions) over different classes of random graphs.
On Large Deviation Properties of Erdös–Rényi Random Graphs
We show that large deviation properties of Erdös-Rényi random graphs can be derived from the free energy of the q-state Potts model of statistical mechanics. More precisely the Legendre transform of…
Complete analysis of phase transitions and ensemble equivalence for the Curie-Weiss-Potts model
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 nearest-neighbor Potts model. It is…
On first-order phase transitions in microcanonical and canonical non-extensive systems
The Bethe lattice spin glass revisited
Abstract:So far the problem of a spin glass on a Bethe lattice has been solved only at the replica symmetric level, which is wrong in the spin glass phase. Because of some technical difficulties,…
Potts Models on Feynman Diagrams
We investigate numerically and analytically Potts models on `thin' random graphs - generic Feynman diagrams, using the idea that such models may be expressed as the limit of a matrix model. The thin…
Microcanonical Thermodynamics: Phase Transitions in 'Small' Systems
- Chemistry, Physics
The mechanical basis of thermodynamics micro-canonical thermodynamics of phase transitions studied in the Potts model liquid-gas transition and surface tension under constant pressure statistical…
Large Deviation Principles and Complete Equivalence and Nonequivalence Results for Pure and Mixed Ensembles
We consider a general class of statistical mechanical models of coherent structures in turbulence, which includes models of two-dimensional fluid motion, quasi-geostrophic flows, and dispersive…