Related papers: Phase transitions and configuration space topology
A thermodynamic phase transition denotes a drastic change of state of a physical system due to a continuous change of thermodynamic variables, as for instance pressure and temperature. The classical van der Waals equation of state is the…
We review the current issues of nonequilibrium phase transitions, in particular, in the early universe. Phase transitions cannot maintain thermal equilibrium and become nonequilibrium when the thermal relaxation time scale is greater than…
Using the formalism of geometrothermodynamics, we investigate the geometric properties of the equilibrium manifold for diverse thermodynamic systems. Starting from Legendre invariant metrics of the phase manifold, we derive thermodynamic…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the $N-$body phase space with the given total energy. Due to Boltzmann's principle,…
One of the important characteristics of topological phases of matter is the topology of the underlying manifold on which they are defined. In this paper, we present the sensitivity of such phases of matter to the underlying topology, by…
The most important recent results in the theory of phase transitions and quantum effects in quantum anharmonic crystals are presented and discussed. In particular, necessary and sufficient conditions for a phase transition to occur at some…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the N-body phase space with the given total energy. Due to Boltzmann's principle,…
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…
Phase transitions of first and second order can easily be distinguished in small systems in the microcanonical ensemble. Configurations of phase coexistence, which are suppressed in the canonical formulation, carry important information…
Topological phase transitions track changes in topological properties of a system and occur in real materials as well as quantum engineered systems, all of which differ greatly in terms of dimensionality, symmetries, interactions, and…
We show that a large class of nonequilibrium many-body systems in contact with two thermal baths admit an exact mapping onto equivalent equilibrium systems. This mapping provides direct access to nonequilibrium phase transition points from…
The Hamiltonian dynamics associated to classical, planar, Heisenberg XY models is investigated for two- and three-dimensional lattices. Besides the conventional signatures of phase transitions, here obtained through time averages of…
Microcanonical thermodynamics (MCTh) is contrasted to canonical thermodynamics (CTh). At phase transitions of 1.order the two ensembles are NOT equivalent even in the thermodynamic limit . Energy fluctuations do not vanish and phase…
A new formulation of statistical mechanics is put forward according to which a random variable characterizing a macroscopic body is postulated to be infinitely divisible. It leads to a parametric representation of partition function of an…
Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were…
Topological quantum phase transitions are characterised by changes in global topological invariants. These invariants classify many body systems beyond the conventional paradigm of local order parameters describing spontaneous symmetry…
We show that thermodynamics can be formulated naturally from the intrinsic geometry of phase space alone-without postulating an ensemble, which instead emerges from the geometric structure itself. Within this formulation, phase transitions…
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…
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…
We overview the concept of dynamical phase transitions in isolated quantum systems quenched out of equilibrium. We focus on non-equilibrium transitions characterized by an order parameter, which features qualitatively distinct temporal…