Related papers: Microcanonical phase transitions for the vortex sy…
The development of reliable methods for estimating microcanonical averages constitutes an important issue in statistical mechanics. One possibility consists of calculating a given microcanonical quantity by means of typical relations in the…
Microcanonical Thermodynamics allows the application of Statistical Mechanics on one hand to closed finite and even small systems and on the other to the largest,self-gravitating ones. However, one has to reconsider the fundamental…
This paper reviews a number of fundamental connections that exist between nonequivalent microcanonical and canonical ensembles, the appearance of first-order phase transitions in the canonical ensemble, and thermodynamic metastable…
Two known distinct examples of one-dimensional systems which are known to exhibit a phase transition are critically examined: (A) a lattice model with harmonic nearest-neighbor elastic interactions and an on-site Morse potential, and (B)…
Using group theory arguments and numerical simulations, we demonstrate the possibility of changing the vorticity or topological charge of an individual vortex by means of the action of a system possessing a discrete rotational symmetry of…
In contrast to the canonical ensemble where thermodynamic functions are smooth for all finite system sizes, the microcanonical entropy can show nonanalytic points also for finite systems, even if the Hamiltonian is smooth. The relation…
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 compare the transition barrier that accompanies a first-order phase transition in the canonical and microcanonical ensemble. This is directly encoded in the probability distributions of standard Metropolis Monte Carlo simulations and a…
The basic quantity for the description of the statistical properties of physical systems is the density of states or equivalently the microcanonical entropy. Macroscopic quantities of a system in equilibrium can be computed directly from…
Most common types of symmetry breaking in quasi-one-dimensional electronic systems possess a combined manifold of states degenerate with respect to both the phase $\theta$ and the amplitude $A$ sign of the order parameter $A\exp(i\theta)$.…
Equilibrium phase transitions may be defined as nonanalytic points of thermodynamic functions, e.g., of the canonical free energy. Given a certain physical system, it is of interest to understand which properties of the system account for…
We discuss the nature of phase transitions in self-gravitating systems both in the microcanonical and in the canonical ensemble. We avoid the divergence of the gravitational potential at short distances by considering the case of…
The vortex states in a thin mesoscopic disk are investigated within the phenomenological Ginzburg-Landau theory in the presence of different ''model'' magnetic field profiles with zero average field which may result from a ferromagnetic…
In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the…
The thermodynamics of the discrete nonlinear Schr\"odinger equation in the vicinity of infinite temperature is explicitly solved in the microcanonical ensemble by means of large-deviation techniques. A first-order phase transition between a…
Systems with long-range as well with short-range interactions should necessarily have a convex entropy S(E) at proper phase transitions of first order, i.e. when a separation of phases occurs. Here the microcanonical heat capacity c(E)=…
In the general case of a many-body Hamiltonian system, described by an autonomous Hamiltonian $H$, and with $K\geq 0$ independent conserved quantities, we derive the microcanonical thermodynamics. By a simple approach, based on the…
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 interactions is solved exactly both for…
We discuss the implications of finite size effects on the determination of the order of a phase transition which may occur in infinite systems. We introduce a specific model to which we apply different tests. They are aimed to characterise…
We consider interacting vortices in a quasi-one-dimensional array of Josephson junctions with small capacitance. If the charging energy of a junction is of the order of the Josephson energy, the fluctuations of the superconducting order…