Ground-state structure in a highly disordered spin-glass model

Journal Article · Thu Feb 01 04:00:00 EST 1996 · Journal of Statistical Physics

DOI:https://doi.org/10.1007/BF02179805· OSTI ID:229703

Newman, C M ^[1]; Stein, D L ^[2]

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1. New York Univ., NY (United States)
2. Univ. of Arizona, Tucson, AZ (United States)

We propose a new Ising spin-glass model on Z{sup d} of Edwards-Anderson type, but with highly disordered coupling magnitudes, in which a greedy algorithm for producing ground states is exact. We find that the procedure for determining (infinite-volume) ground states for this model can be related to invasion percolation with the number of ground states identified as 2{sup N}, where N = N (d) is the number of distinct global components in the {open_quotes}invasion forest{close_quotes}. We prove that N(d)= {infinity} is d{sub c}=8. When N(d)={infinity}, we consider free or periodic boundary conditions on cubes of side length L and show that frustration leads to chaotic L dependence with all pairs of ground states occurring as subsequence limits. We briefly discuss applications of our results to random walk problems on rugged landscapes.

• Sponsoring Organization: USDOE
• DOE Contract Number: FG03-93ER25155
• OSTI ID: 229703
• Journal Information: Journal of Statistical Physics, Journal Name: Journal of Statistical Physics Journal Issue: 3-4 Vol. 82; ISSN JSTPBS; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ALGORITHMS
GROUND STATES
ISING MODEL
MATHEMATICAL MODELS