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. Schakel2 — 1Institut 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.