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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 dc. 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<dc=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 dc, 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)

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