Dresden 2006 – scientific programme

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DY: Dynamik und Statistische Physik

DY 40: Critical Phenomena and Phase Transitions I

DY 40.2: Talk

Thursday, March 30, 2006, 10:00–10:15, H\"UL 186

On the breakdown of finite-size scaling in high dimensional 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, both in equilibrium (e.g. the Ising model, see [1] for an overview) and non-equilibrium (e.g. directed percolation [2]). Less work was done for geometric phase transitions and for Dirichlet boundary conditions. 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, whereas it exceeds the systems size 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] X. S. Chen and V. Dohm, Phys. Rev. E 63, 016113 (2000)

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