Spin-glass model with dimension-dependent ground state multiplicity

Journal Article · Mon Apr 04 04:00:00 EDT 1994 · Physical Review Letters; (United States)

DOI:https://doi.org/10.1103/PhysRevLett.72.2286· OSTI ID:5011060

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. Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States) Department of Physics, University of Arizona, Tucson, Arizona 85721 (United States)

We introduce a new Ising spin-glass model and use it to study the relation between quenched disorder, frustration, ground state mulitplicity, and dimension. The Hamiltonian is of Edwards-Anderson type in any finite volume but the coupling magnitudes scale nonlinearly with volume. We find a mapping between the ground state structure of this model and the global connectivity structure of invasion percolation in the same dimension. We argue that our model has a singular pair of ground states below eight dimensions and infinitely many above.

• DOE Contract Number: FG03-93ER25155
• OSTI ID: 5011060
• Journal Information: Physical Review Letters; (United States), Journal Name: Physical Review Letters; (United States) Vol. 72:14; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CRYSTAL MODELS
DIMENSIONS
ENERGY LEVELS
GROUND STATES
ISING MODEL
MAGNETISM
MATHEMATICAL MODELS
QUENCHING
SPIN GLASS STATE