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
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 ds 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.
PACS: 75.10.Nr – Spin-glass and other random models
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001