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

Ground-state structure in a highly disordered spin-glass model We propose a new Ising spin-glass model on Z 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 N , whereN=N(d) is the number of distinct global components in the “invasion forest.” We prove thatN(d)=∞ if the invasion connectivity function is square summable. We argue that the critical dimension separatingN=1 andN=∞ isd c=8. WhenN(d)=∞, we consider free or periodic boundary conditions on cubes of side lengthL and show that frustration leads to chaoticL dependence withall pairs of ground states occurring as subsequence limits. We briefly discuss applications of our results to random walk problems on rugged landscapes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Statistical Physics Springer Journals

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

Journal of Statistical Physics , Volume 82 (4) – Sep 2, 2005

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References (52)

Publisher
Springer Journals
Copyright
Copyright
Subject
Physics; Statistical Physics and Dynamical Systems; Theoretical, Mathematical and Computational Physics; Physical Chemistry; Quantum Physics
ISSN
0022-4715
eISSN
1572-9613
DOI
10.1007/BF02179805
Publisher site
See Article on Publisher Site

Abstract

We propose a new Ising spin-glass model on Z 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 N , whereN=N(d) is the number of distinct global components in the “invasion forest.” We prove thatN(d)=∞ if the invasion connectivity function is square summable. We argue that the critical dimension separatingN=1 andN=∞ isd c=8. WhenN(d)=∞, we consider free or periodic boundary conditions on cubes of side lengthL and show that frustration leads to chaoticL dependence withall pairs of ground states occurring as subsequence limits. We briefly discuss applications of our results to random walk problems on rugged landscapes.

Journal

Journal of Statistical PhysicsSpringer Journals

Published: Sep 2, 2005

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