The $\pm J $ spin glass in Migdal-Kadanoff approximation

Details The $\pm J $ spin glass in Migdal-Kadanoff approximation The $\pm J $ spin glass in Migdal-Kadanoff approximation

2001-02-18

arxiv.org/abs/cond-mat/0102317v1

Physics

Condensed Matter

Statistical Mechanics

6 pages RevTex, 6 postscript figures

Scientific paper

10.1007/s100510170169

We study the low-temperature phase of the three-dimensional $\pm J$ Ising spin glass in Migdal-Kadanoff approximation. At zero temperature, T=0, the properties of the spin glass result from the ground-state degeneracy and can be elucidated using scaling arguments based on entropy. The approach to the asymptotic scaling regime is very slow, and the correct exponents are only visible beyond system sizes around 64. At T>0, a crossover from the zero-temperature behaviour to the behaviour expected from the droplet picture occurs at length scales proportional to $T^{-d_s/2}$ where $d_s$ is the fractal dimension of a domain wall. Canonical droplet behaviour is not visible at any temperature for systems whose linear dimension is smaller than 16 lattice spacings, because the data are either affected by the zero-temperature behaviour or the critical point behaviour.

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