Related papers: Effective negative specific heat by destabilizatio…
According to thermodynamics, the specific heat of Boltzmannian short-range interacting systems is a positive quantity. Less intuitive properties are instead displayed by systems characterized by long-range interactions. In that case, the…
We study non-canonical relaxation in a composite cold atoms system, consisting of subsystems that possess negative microcanonical specific heat. The system exhibits pre-thermalization far away from integrability due to the appearance of a…
In this micro-canonical simulation the temperature and also the specific heat are determined as averages of expressions easy to implement. The XY-chain is studied for a test. The second order transition on a cubic lattice and the first…
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…
While the canonical ensemble has been tremendously successful in capturing thermal statistics of macroscopic systems, deviations from canonical behavior exhibited by small systems are not well understood. Here, using a small two dimensional…
We show how to generalise the zero temperature Lanczos method for calculating dynamical correlation functions to finite temperatures. The key is the microcanonical ensemble, which allows us to replace the involved canonical ensemble with a…
Equilibrium statistics of finite Hamiltonian systems is fundamentally described by the microcanonical ensemble (ME). Canonical, or grand-canonical partition functions are deduced from this by Laplace transform. Only in the thermodynamic…
A system of globally coupled rotors is studied in a unified framework of microcanonical and canonical ensembles. We consider the Fokker-Planck equation governing the time evolution of the system, and examine various stationary as well as…
We develop a scaling theory for the finite-size critical behavior of the microcanonical entropy (density of states) of a system with a critically-divergent heat capacity. The link between the microcanonical entropy and the canonical energy…
Monte Carlo simulations have boosted the numerical study of several different physical systems and in particular, the canonical ensemble has been especially useful because of the existence of easy and efficient relaxation algorithms…
It is typically assumed, without justification, that a weak coupling between a system and a bath is a necessary condition for the equivalence of a canonical ensemble and a microcanonical ensemble. For instance, in a canonical ensemble,…
The grand canonical ensemble lies at the core of quantum and classical statistical mechanics. A small system thermalizes to this ensemble while exchanging heat and particles with a bath. A quantum system may exchange quantities represented…
We consider the statistical mechanics of a small gaseous system subject to a constant external field. As is well known, in the canonical ensemble the system i) obeys a barometric formula for the density profile and ii) the kinetic…
In this paper we discuss how partial knowledge of the density of states for a model can be used to give good approximations of the energy distributions in a given temperature range. From these distributions one can then obtain the…
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 have used a toy model to study the behaviour of confined binary systems in 2$D$ and compare it with previously known result in 3$D$. In the case of 2$D$, in which canonical distribution exists only above a critical temperature, we…
We study the thermodynamics of the Hamiltonian Mean Field (HMF) model with an external potential playing the role of a "magnetic field". If we consider only fully stable states, this system does not present any phase transition. However, if…
A well-established numerical technique to study the dynamics of spin systems in which symmetries and conservation laws play an important role is to microcanonically integrate their reversible equations of motion, obtaining thermalization…
Specific heat measurements down to 120mK have been performed on a quasi-one-dimensional $S=1/2$ spin-gapped system (CH$_3$)$_2$NH$_2$CuCl$_3$ in a magnetic field up to 8 T. This compound has a characteristic magnetization curve which shows…
The thermodynamic properties of bosons moving in a harmonic trap in an arbitrary number of dimensions are investigated in the grand canonical, canonical and microcanonical ensembles by applying combinatorial techniques developed earlier in…