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DY: Dynamik und Statistische Physik

DY 23: Symposium Renormalization and Scaling (SYRS) – Contributed Talks I

DY 23.2: Talk

Saturday, March 5, 2005, 14:15–14:30, TU H3010

Fractal structure and critical properties of planar loops — •Adriaan Schakel and Wolfhard Janke — Institut fuer Theoretische Physik, Universitaet Leipzig, Augustusplatz 10/11, 04109 Leipzig

The fractal structure of random loops formed by the high-temperature graphs of the two-dimensional O(N) model at the critical point are investigated by means of Monte Carlo simulations. At high temperatures, the loops have a finite line tension and are exponentially suppressed. Upon approaching the critical point, they gradually grow in size until reaching the critical point where the line tension vanishes and the loops proliferate–much like the sudden appearance of a spanning cluster at the percolation threshold in percolation phenomena. De Gennes’ results for polymer chains, corresponding to the limit N → 0, are generalized to arbitrary −2 ≤ N ≤ 2. The fractal structure of these loops is shown to encode the entire critical behavior of the O(N) models. The loops are also studied close to their tricritical point, corresponding to the Θ point in the context of polymers, where they collapse. A close connection between the fractal structures and thus the two critical behaviors is established.