Energy exponents and corrections to scaling in Ising spin glasses

Details Energy exponents and corrections to scaling in Ising spin glasses Energy exponents and corrections to scaling in Ising spin glasses

2002-12-03

arxiv.org/abs/cond-mat/0212070v2

Phys. Rev. B 68, 224404 (2003).

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages, RevTex, 9 figures

Scientific paper

10.1103/PhysRevB.68.224404

We study the probability distribution P(E) of the ground state energy E in various Ising spin glasses. In most models, P(E) seems to become Gaussian with a variance growing as the system's volume V. Exceptions include the Sherrington-Kirkpatrick model (where the variance grows more slowly, perhaps as the square root of the volume), and mean field diluted spin glasses having +/-J couplings. We also find that the corrections to the extensive part of the disorder averaged energy grow as a power of the system size; for finite dimensional lattices, this exponent is equal, within numerical precision, to the domain-wall exponent theta_DW. We also show how a systematic expansion of theta_DW in powers of exp(-d) can be obtained for Migdal-Kadanoff lattices. Some physical arguments are given to rationalize our findings.

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