3D Spin Glass and 2D Ferromagnetic XY Model: a Comparison

Details 3D Spin Glass and 2D Ferromagnetic XY Model: a Comparison 3D Spin Glass and 2D Ferromagnetic XY Model: a Comparison

1997-07-04

arxiv.org/abs/cond-mat/9707050v1

Journal of Physics A:Math and Gen. 30 (1997) 7337

Physics

Condensed Matter

Disordered Systems and Neural Networks

14 pages and 6 figures. Also available at http://chimera.roma1.infn.it/index_papers_complex.html

Scientific paper

10.1088/0305-4470/30/21/010

We compare the probability distributions and Binder cumulants of the overlap in the 3D Ising spin glass with those of the magnetization in the ferromagnetic 2D XY model. We analyze similarities and differences. Evidence for the existence of a phase transition in the spin glass model is obtained thanks to the crossing of the Binder cumulant. We show that the behavior of the XY model is fully compatible with the Kosterlitz-Thouless scenario. Finite size effects have to be dealt with by using great care in order to discern among two very different physical pictures that can look very similar if analyzed without large attention.

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