The Link Overlap and Finite Size Effects for the 3D Ising Spin Glass

Details The Link Overlap and Finite Size Effects for the 3D Ising Spin Glass The Link Overlap and Finite Size Effects for the 3D Ising Spin Glass

1999-05-25

arxiv.org/abs/cond-mat/9905354v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

7 pages, 10 figures

Scientific paper

10.1007/s100510050043

We study the link overlap between two replicas of an Ising spin glass in three dimensions using the Migdal-Kadanoff approximation and scaling arguments based on the droplet picture. For moderate system sizes, the distribution of the link overlap shows the asymmetric shape and large sample-to-sample variations found in Monte Carlo simulations and usually attributed to replica symmetry breaking. However, the scaling of the width of the distribution, and the link overlap in the presence of a weak coupling between the two replicas are in agreement with the droplet picture. We also discuss why it is impossible to see the asymptotic droplet-like behaviour for moderate system sizes and temperatures not too far below the critical temperature.

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