Eur. Phys. J. B 21, 589-594 (2001)
https://doi.org/10.1007/s100510170169

The ±J spin glass in Migdal-Kadanoff approximation

¹ School of Physics and Astronomy, Raymond and Beverley Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel
² Department of Physics, University of Manchester, Manchester M13 9PL, UK

Corresponding author: ^a barbara@gina.tau.ac.il

Received: 18 February 2001
Published online: 15 June 2001

Abstract

We study the low-temperature phase of the three-dimensional ±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 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.