Heidelberg 1999 – wissenschaftliches Programm

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 8: Statistische Mechanik

MP 8.1: Fachvortrag

Freitag, 19. März 1999, 14:00–14:20, MA1

Exact partition functions for the primitive droplet nucleation model in 2 and 3 dimensions — •Hans Kastrup — Institut für Theoretische Physik, RWTH Aachen, 52056 Aachen

The grand canonical partition functions for primitive droplet nucleation

models with an excess energy є_n = − µn+σ n^1−η,  η = 1/d, for droplets of n constitutents (e.g. Ising spins) in d dimensions are calculated exactly in closed form (integral representations) for d=2 and d=3 for all complex µ by exploiting the fact that the partition functions obey simple linear partial differential equations.

For large β=1/(k_B T) the exact imaginary part of the partition functions coincides with the long known saddle point approximations.
For d=2 the classical grand canonical partition function of the droplet

nucleation model coincides with the quantum canonical partition function for Schwarzschild black holes in 4 space-time dimensions. The latter partition function implies the Hawking temperature and the Bekenstein-Hawking entropy.
Ref.: Phys. Rev. Lett. 81(1998)2280