Related papers: Extended gaussian ensemble solution and tricritica…
We have investigated the time-dependent regime of a two-dimensional metamagnetic model at its tricritical point via Monte Carlo simulations. First of all, we obtained the temperature and magnetic field corresponding to the tricritical point…
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…
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…
We study the effect of competing interactions on ensemble inequivalence. We consider a one-dimensional Ising model with ferromagnetic mean-field interactions and short-range nearest-neighbor and next-nearest-neighbor couplings which can be…
The microcanonical ensemble is a natural starting point of statistical mechanics. However, when it comes to perturbation theory in statistical mechanics, traditionally only the canonical and grand canonical ensembles have been used. In this…
We discuss a generalized quantum microcanonical ensemble. It describes isolated systems that are not necessarily in an eigenstate of the Hamilton operator. Statistical averages are obtained by a combination of a time average and a maximum…
Ensemble inequivalence has been observed in several systems. In particular it has been recently shown that negative specific heat can arise in the microcanonical ensemble in the thermodynamic limit for systems with long-range interactions.…
The non-extensive statistical mechanics has been used to describe a variety of complex systems. The maximization of entropy, often used to introduce the non-extensive statistical mechanics, is a formal procedure and does not easily leads to…
In the field of classical discrete systems, specifically substitutional alloys, this study introduces a stochastic thermodynamic approach to address nonlinearity within a canonical ensemble. This approach establishes a nonlinear…
The present work extends the well-known thermodynamic relation $C=\beta ^{2}< \delta {E^{2}}>$ for the canonical ensemble. We start from the general situation of the thermodynamic equilibrium between a large but finite system of interest…
We propose a generalized Dicke model which supports a quantum tricritical point. We map out the phase diagram and investigate the critical behaviors of the model through exact low-energy effective Hamiltonian in the thermodynamic limit. As…
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…
For more than 100 years, one of the central concepts in statistical mechanics has been the microcanonical ensemble, which provides a way of calculating the thermodynamic entropy for a specified energy. A controversy has recently emerged…
The integrable system is constrained strictly by the conservation law during the time evolution, and the nearly integrable system or nonintegrable system is also constrained by the conserved parameters (like the constants of motion) with…
The framework of non-extensive statistical mechanics, proposed by Tsallis, has been used to describe a variety of systems. The non-extensive statistical mechanics is usually introduced in a formal way, using the maximization of entropy. In…
The microcanonical properties of a two dimensional system of N classical particles interacting via a smoothed Newtonian potential as a function of the total energy E and the total angular momentum L are discussed. In order to estimate…
We investigate the spin-$1$ Blume-Capel model on an infinite strip of the triangular lattice using the transfer-matrix method combined with a sparse-matrix factorization technique. Through finite-size scaling analysis of numerically exact…
The entropy definition in the microcanonical ensemble is revisited. We propose a novel definition for the microcanonical entropy that resolve the debate on the correct definition of the microcanonical entropy. In particular we show that…
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…
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…