Regensburg 2004 – scientific programme

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DY: Dynamik und Statistische Physik

DY 16: Phase Transitions

DY 16.4: Talk

Monday, March 8, 2004, 17:30–17:45, H2

On the Structure of Microcanonical Entropy Surfaces of Finite Systems — •Hans Behringer — Institut für Theoretische Physik I, Universität Erlangen-Nürnberg, Staudtstrasse 7, D - 91058 Erlangen, Germany

The basic quantity in the microcanonical approach to statistical properties of magnetic systems is the entropy S(E, M) = lnΩ(E, M) where Ω(E,M) is the density of states. The spontaneous magnetization and the response functions like the magnetic susceptibility and the specific heat are obtained from the curvature properties of the entropy surface. Even for finite system sizes they show features which are typical of phase transitions. The appearance of classical exponents characterising the singularities of thermostatic quantities of finite systems can be understood from the analyticity of the entropy surface. Symmetry properties of the microcanonical entropy are deduced directly from the invariance group of the Hamiltonian. These properties allow further general statements on the global structure of the entropy surface.

[1] H. Behringer, Symmetries of Microcanonical Entropy Surfaces, J. Phys. A: Math. Gen. 36, 8739 (2003)

[2] H. Behringer, Microcanonical Entropy for Small Magnetisations, to appear in J. Phys. A, preprint cond-mat/0311211