Related papers: Remarks about the Phase Transitions within the Mic…
We consider a Hamiltonian system made of $N$ classical particles moving in two dimensions, coupled via an {\it infinite-range interaction} gauged by a parameter $A$. This system shows a low energy phase with most of the particles trapped in…
This article characterizes phase transitions in temperature within a specific space of H\"older continuous potentials, distinguished by their regularity and asymptotic behavior at zero. We also characterize the phase transitions in…
The thermodynamical properties of a generalized Dicke model are calculated and related with the critical properties of its energy spectrum, namely the quantum phase transitions (QPT) and excited state quantum phase transitions (ESQPT). The…
Non-extensive systems do not allow to go to the thermodynamic limit. Therefore we have to reformulate statistical mechanics without invoking the thermodynamical limit. I.e. we have to go back to Pre-Gibbsian times. We show that Boltzmann's…
The microscopic model in which nodes interacting with each other are statistical systems is introduced. The nodes conditions are connected with a string of distinct microscopic configurations and depend on external parameters (pressure and…
The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…
We address the question of the quantitative relationship between thermodynamic phase transitions and topological changes in the potential energy manifold analyzing two classes of one dimensional models, the Burkhardt solid-on-solid model…
Topological phase transitions, characterized by the closing and reopening of band gaps and a concomitant change in topological invariants, have played a central role in topological physics. However, such transitions have so far been…
Phase transitions are conventionally defined by nonanalyticities of thermodynamic potentials in the thermodynamic limit. In this Letter, we show that the singularity is not the definition of criticality but its asymptotic outcome:…
Microcanonical analysis is a powerful method for studying phase transitions of finite-size systems. This method has been used so far only for studying phase transitions of equilibrium systems, which can be described by microcanonical…
Two mathematical mechanisms, responsible for the generation of a thermodynamic singularity, are individuated. For a class of short-range, confining potentials, a topology change in some family of configuration space submanifolds is the only…
Many quantum condensed-matter systems, and probably the quantum vacuum of our Universe, are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, physics which emerges in the…
By means of the principle of minimal sensitivity we generalize the microcanonical inflection-point analysis method by probing derivatives of the microcanonical entropy for signals of transitions in complex systems. A strategy of…
Phase transitions generically occur in random matrix models as the parameters in the joint probability distribution of the random variables are varied. They affect all main features of the theory and the interpretation of statistical models…
We develop a geometric theory of phase transitions (PTs) for Hamiltonian systems in the microcanonical ensemble. This theory allows to reformulate Bachmann's classification of PTs for finite-size systems in terms of geometric properties of…
Transition out of a topological phase is typically characterized by discontinuous changes in topological invariants along with bulk gap closings. However, as a clean system is geometrically punctured, it is natural to ask the fate of an…
Boltzmann's principle S(E,N,V...)=ln W(E,N,V...) allows the interpretation of Statistical Mechanics of a closed system as Pseudo-Riemannian geometry in the space of the conserved parameters E,N,V... (the conserved mechanical parameters in…
We study the phase transition between a trivial and a time-reversal-invariant topological superconductor in a single-band system. By analyzing the interplay of symmetry, topology and energetics, we show that for a generic normal state band…
In this paper, we investigate signatures of topological phase transitions in interacting systems. We show that the key signature is the existence of a topologically protected level crossing, which is robust and sharply defines the…
Aggregation transitions in disordered mesoscopic systems play an important role in several areas of knowledge, from materials science to biology. The lack of a thermodynamic limit in systems that are intrinsically finite makes the…