Berlin 2012 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 31: Phase Transitions and Critical Phenomena

DY 31.2: Talk

Friday, March 30, 2012, 10:00–10:15, MA 004

Loop percolation — •Matthias J. F. Hoffmann, Susan Nachtrab, Gerd E. Schröder-Turk, and Klaus Mecke — Institut für Theoretische Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen

We report a new planar percolation model, called loop percolation, which is in a different universality class than the conventional bond- or site percolation models. The model is defined by randomly disconnecting, with probability p, the degree-four nodes of a planar square lattice into two unconnected degree-two nodes; for each disconnection, the two possible orientations are chosen randomly with the probability x=1/2. The extremal configurations are the periodic square lattice (at p=0 with no disconnected nodes) and a configuration of many self-avoiding unbranched random walks, “spaghetti state”, when all nodes are disconnected at p=1. Numerical analysis shows that this model has a percolation transition at p_c=1, that is, only when all nodes are disconnected. The critical exponents (β=1/3, ν = 4/3, γ=67/36, D_f=79/48) of this transition are numerically shown to be significantly different from those of the conventional bond- or site-percolation model, and to agree with a mapping to the six-vertex model. Further, when suitably generalized to x≠ 1/2 the model shows a percolation transition at p_c=(1+|2x−1|)⁻¹ with the critical bond/site percolation exponents for all x≠ 1/2.