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Dresden 2006 – scientific programme

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DY: Dynamik und Statistische Physik

DY 42: Critical Phenomena and Phase Transitions II

DY 42.1: Talk

Thursday, March 30, 2006, 11:00–11:15, H\"UL 186

Fortuin-Kasteleyn versus geometrical cluster — •Wolfhard Janke1 and Adriaan M.J. Schakel21Institut für Theoretische Physik, Universität Leipzig, Augustusplatz 10/11, 04109 Leipzig — 2Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin

We discuss how suitably defined geometrical objects encode in their fractal structure thermal critical behaviour [1]. Emphasis will be placed on the two-dimensional Potts model for which two types of spin clusters can be defined. Whereas the Fortuin-Kasteleyn clusters describe the standard critical behaviour of the pure model, the geometrical clusters describe the tricritical behaviour that arises when including vacant sites in the pure Potts model. The close connection between the two models respectively the two cluster types can be explained by a “dual map” that conserves the central charge, so that both model/cluster types are in the same universality class. The geometrical picture is supported by Monte Carlo simulations.

[1] W. Janke and A.M.J. Schakel, Nucl. Phys. B700, 385 (2004); Phys. Rev. E71, 036703 (2005); Phys. Rev. Lett. 95, 135702 (2005); and e-print cond-mat/0508734.

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