Related papers: Optimization of finite-size errors in finite-tempe…
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 introduce a quantum Monte Carlo method at finite temperature for interacting fermionic models in the canonical ensemble, where the conservation of the particle number is enforced. Although general thermodynamic arguments ensure the…
We investigate the critical scaling behavior of finite systems in the canonical ensemble. The essential difference with the grand canonical ensemble. i.e., the constraint on the number of particles, is already known to lead to the Fisher…
The thermodynamical cluster model is known to present a first-order liquid-gas phase transition in the idealized case of an uncharged, infinitely extended medium. However, in most practical applications of this model, the system is finite…
Grand canonical and canonical ensembles become equivalent in the thermodynamic limit, but when the system size is finite the results obtained in the two ensembles deviate from each other. In many important cases, the canonical ensemble…
We study finite size effects in a family of systems in which a parameter controls interaction-range. In the long-range regime where the infinite-size free energy is universal, we show that the finite size effects are not universal but…
A new method is proposed for a treatment of ideal quantum gases in the microcanonical ensemble near the thermodynamic limit. The method allows rigorous asymptotic calculations of the average number of particles and particle number…
We provide the first rigorous study of the finite-size error in the simplest and representative coupled cluster theory, namely the coupled cluster doubles (CCD) theory, for gapped periodic systems. Assuming that the CCD equations are solved…
We study the Bose-Einstein condensation phase transition in a weakly interacting gas through a perturbative analysis of finite systems. In both the grand canonical and the canonical ensembles, perturbation theory suffers from infrared…
For models which exhibit a continuous phase transition in the thermodynamic limit a numerical study of small systems reveals a non-monotonic behaviour of the microcanonical specific heat as a function of the system size. This is in contrast…
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…
We discuss the finite size behaviour in the canonical ensemble of the balls in boxes model. We compare theoretical predictions and numerical results for the finite size scaling of cumulants of the energy distribution in the canonical…
The thermodynamics for a system with given temperature, density, and volume is described by the Canonical ensemble. The thermodynamics for a corresponding system with the same temperature, volume, and average density is described by the…
The properties of isobaric ratios, between nuclei produced in the same reaction, are investigated using the canonical and grand-canonical statistical ensembles. Although the grand-canonical for- mulae furnish a means to correlate the ratios…
Molecular dynamics simulations are performed for a supercooled simple liquid with changing the system size from N=108 to $10^4$ to examine possible finite-size effects. Although almost no systematic deviation is detected in the static pair…
We investigate the relation between various statistical ensembles of finite systems. If ensembles differ at the level of fluctuations of the order parameter, we show that the equations of states can present major differences. A sufficient…
We compare phase transition(-like) phenomena in small model systems for both microcanonical and canonical ensembles. The model systems correspond to a few classical (non-quantum) point particles confined in a one-dimensional box and…
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…
In the realm of statistical mechanics, it has been established that there is no distinction between the micro-canonical and canonical ensembles in the thermodynamic limit. However, this paradigm may alter when addressing statistical…
The microcanonical ensemble is in important physical situations different from the canonical one even in the thermodynamic limit. In contrast to the canonical ensemble it does not suppress spatially inhomogeneous configurations like phase…