Finite-size corrections for ground states of Edwards-Anderson spin glasses

Abstract

Extensive computations of ground-state energies of the Edwards-Anderson spin glass on bond-diluted, hypercubic lattices are conducted in dimensions d=3, …, 7. Results are presented for bond densities exactly at the percolation threshold, p=pc, and deep within the glassy regime, p>pc, where finding ground states is one of the hardest combinatorial optimization problems. Finite-size corrections of the form 1/Nω are shown to be consistent throughout with the prediction ω=1−y/d, where y refers to the “stiffness” exponent that controls the formation of domain wall excitations at low temperatures. At p=pc, an extrapolation for d→∞ appears to match our mean-field results for these corrections. In the glassy phase, however, ω does not approach its anticipated mean-field value of 2/3, obtained from simulations of the Sherrington-Kirkpatrick spin glass on an N-clique graph. Instead, the value of ω reached at the upper critical dimension matches another type of mean-field spin glass models, namely those on sparse random networks of regular degree called Bethe lattices.