Simplicity of state and overlap structure in finite-volume realistic spin glasses

Journal Article · Sun Feb 01 04:00:00 EST 1998 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.57.1356· OSTI ID:591804

Newman, C M ^[1]; Stein, D L ^[2]

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1. Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)
2. Departments of Physics and Mathematics, University of Arizona, Tucson, Arizona 85721 (United States)

We present a combination of heuristic and rigorous arguments indicating that both the pure state structure and the overlap structure of realistic spin glasses should be relatively simple: in a large finite volume with coupling-independent boundary conditions, such as periodic, at most a pair of flip-related (or the appropriate number of symmetry-related in the non-Ising case) states appear, and the Parisi overlap distribution correspondingly exhibits at most a pair of {delta} functions at {plus_minus}q{sub EA}. This rules out the nonstandard mean-field picture introduced by us earlier, and when combined with our previous elimination of more standard versions of the mean-field picture, argues against the possibility of even limited versions of mean-field ordering in realistic spin glasses. If broken spin-flip symmetry should occur, this leaves open two main possibilities for ordering in the spin glass phase: the droplet-scaling two-state picture, and the chaotic pairs many-state picture introduced by us earlier. We present scaling arguments which provide a possible physical basis for the latter picture, and discuss possible reasons behind numerical observations of more complicated overlap structures in finite volumes. {copyright} {ital 1998} {ital The American Physical Society}

• OSTI ID: 591804
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 2 Vol. 57; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BOUNDARY CONDITIONS
MEAN-FIELD THEORY
SPIN FLIP
SPIN GLASS STATE