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=p_c, and deep within the glassy regime, p>p_c, where finding ground-states becomes a hard combinatorial problem. Finite-size corrections of the form 1/N^w are shown to be consistent throughout with the prediction w=1-y/d, where y refers to the "stiffness" exponent that controls the formation of domain wall excitations at low temperatures. At p=p_c, an extrapolation for $d\to \infty$ appears to match our mean-field results for these corrections. In the glassy phase, w does not approach the value of 2/3 for large d predicted from simulations of the Sherrington-Kirkpatrick spin glass. However, the value of w reached at the upper critical dimension does match certain mean-field spin glass models on sparse random networks of regular degree called Bethe lattices.

6 pages, RevTex4, all ps figures included, corrected and final version with extended analysis and more data, such as for case d=3. Find additional information at http://www.physics.emory.edu/faculty/boettcher/

Cited by in corpus (7)

• Number of thermodynamic states in the three-dimensional Edwards-Anderson spin glass
• One-dimensional infinite component vector spin glass with long-range interactions
• Ground State Properties of the Diluted Sherrington-Kirkpatrick Spin Glass
• Deep reinforced learning heuristic tested on spin-glass ground states: The larger picture
• Physics of the Edwards-Anderson Spin Glass in Dimensions $d=3,\dots ,8$ from Heuristic Ground State Optimization
• Ground state interface exponents of the diluted Sherrington-Kirkpatrick spin glass
• Optimization by Record Dynamics