Regensburg 2007 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 21: Finite size effects at phase transitions II (session accompanying the symposium of the same name)

DY 21.2: Talk

Wednesday, March 28, 2007, 14:15–14:30, H3

On the breakdown of finite-size scaling in high dimensional periodical systems — •Alfred Hucht and Sven Lübeck — Theoretische Physik, Universität Duisburg-Essen, D-47048 Duisburg

Finite-size scaling functions of continuous phase transitions exhibit a scaling anomaly above the upper critical dimension d_c. This so-called breakdown of finite-size scaling is well-established on the basis of field theoretical and numerical approaches for system with periodic boundary conditions (BC), both in equilibrium (e.g. the Ising model) and non-equilibrium (e.g. directed percolation [1]). Less work was done for geometric phase transitions and for Dirichlet BC. Therefore, we numerically investigate the bond percolation transition in 2 ≤ d ≤ 10 dimensions with various boundary conditions. For d<d_c=6 the spatial correlation length is limited by the systems size at criticality for all BCs, whereas it exceeds the systems size in systems with periodic BC above d_c, the hallmark of the breakdown of finite-size scaling. We present, to our knowledge for the first time, a phenomenological and descriptive interpretation of this breakdown of finite-size scaling. Furthermore, we show that the high-dimensional behavior depends strongly on the boundary conditions.

[1] S. Lübeck and H.-K. Janssen, Phys. Rev. E 72, 016119 (2005)