1,431 research outputs found
Ensemble inequivalence in systems with long-range interactions
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. We display a connection between such behaviour and a mean-field
like structure of the partition function. Since short-range models cannot
display this kind of behaviour, this strongly suggests that such systems are
necessarily non-mean field in the sense indicated here. We illustrate our
results showing an application to the Blume-Emery-Griffiths model. We further
show that a broad class of systems with non-integrable interactions are indeed
of mean-field type in the sense specified, so that they are expected to display
ensemble inequivalence as well as the peculiar behaviour described above in the
microcanonical ensemble.Comment: 12 pages, no figure
Ensemble inequivalence: A formal approach
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. We display a connection between such behaviour and a mean-field
like structure of the partition function. Since short-range models cannot
display this kind of behaviour, this strongly suggests that such systems are
necessarily non-mean field in the sense indicated here. We further show that a
broad class of systems with non-integrable interactions are indeed of
mean-field type in the sense specified, so that they are expected to display
ensemble inequivalence as well as the peculiar behaviour described above in the
microcanonical ensemble.Comment: 4 pages, no figures, given at the NEXT2001 conference on
non-extensive thermodynamic
Spectral correlations in the crossover between GUE and Poisson regularity: on the identification of scales
Motivated by questions of present interest in nuclear and condensed matter
physics we consider the superposition of a diagonal matrix with independent
random entries and a GUE. The relative strength of the two contributions is
determined by a parameter suitably defined on the unfolded scale.
Using results for the spectral two-point correlator of this model obtained in
the framework of the supersymmetry method we focus attention on two different
regimes. For << 1 the correlations are given by Dawson's integral
while for >> 1 we derive a novel analytical formula for the two-point
function. In both cases the energy scales, in units of the mean level spacing,
at which deviations from pure GUE behavior become noticable can be identified.
We also derive an exact expansion of the local level density for finite level
number.Comment: 15 pages, Revtex, no figures, to be published in special issue of J.
Math. Phys. (1997
- …