Dresden 2011 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 42: Critical Phenomena and Phase Transitions
DY 42.7: Talk
Friday, March 18, 2011, 11:45–12:00, ZEU 255
The infinite-component spin glass revisited — •Frank Beyer and Martin Weigel — Institut für Physik, KOMET 331, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, 55127 Mainz
Starting from the Sherrington-Kirkpatrick (SK) mean-field spin-glass model with a broken replica symmetry, an expansion towards finite (spatial) dimensions (d=2,3,…) breaks down at the upper critical dimension. One way of bypassing these problems might be to consider the replica-symmetric m-component vector spin glass in the limit m→∞ and attempt an expansion towards the finite-m cases including the XY and Heisenberg spin glass. In this contribution, we study vector spin glasses in the m→∞ limit using ground-state calculations at zero temperature and a saddle-point approximation at finite temperatures. For the SK model, we show the existence of a finite order parameter in the ordered phase and critical scaling behavior consistent with an upper critical dimension equal to eight. Using ground-state calculations, we determine the lower critical dimension to be 5≤ dl≤ 6 when the limit m→∞ is taken before the thermodynamic limit N→∞, while we find indications for dl = 3 for the opposite (physical) order of taking limits. Complementing these results, we studied a one-dimensional chain with power-law decay of interactions that can be continuously tuned from the mean-field to the short-range regime.