# Dresden 2006 – wissenschaftliches Programm

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# DY: Dynamik und Statistische Physik

## DY 40: Critical Phenomena and Phase Transitions I

### DY 40.3: Vortrag

### Donnerstag, 30. März 2006, 10:15–10:30, H\"UL 186

**Finite-size behaviour of the microcanonical specific heat** — •Hans Behringer^{1} and Michel Pleimling^{2} — ^{1}Fakultät für Physik, Universität Bielefeld, D-33615 Bielefeld — ^{2}Institut für Theoretische Physik I, Universität Erlangen-Nürnberg, D-91058 Erlangen

The basic quantity in the microcanonical approach to statistical
properties of physical systems is the entropy *S*(*E*) = lnΩ(*E*)
where Ω(*E*) is the density of states as a function of the
energy. The specific heat of the system is related to the inverse of
the curvature of the entropy. The behaviour of the
microcanonical specific heat of systems that undergo a continuous
phase transition in the thermodynamic limit is investigated for finite
systems. The numerical study of small Ising and Potts systems reveals
a non-monotonic behaviour of the microcanonical specific heat as a
function of the system size in contrast to a canonical treatment where
the maximum of the specific heat increases monotonically with the
system size. A general phenomenological theory is developed which
permits a description of this peculiar behaviour of the microcanonical
specific heat and allows in principle the determination of the
microcanonical critical exponents from asymptotically large systems.
In the case of the Baxter-Wu model the microcanonical analysis reveals
a behaviour of the specific heat that suggests at first sight the
appearance of a discontinuous phase transition in the infinite volume
limit contrary to the known continuous character. However, the
proposed phenomenological theory shows that this peculiar behaviour
stems from a finite-size effect which disappears in the thermodynamic
limit and therefore the observations are consistent with the
continuous phase transition of in the Baxter-Wu model.