The effective field approximation for Ising spin glasses on simply connected lattices

Guihua Zhang, Jerome Percus

Research output: Contribution to journalArticle

Abstract

A spin glass on a one-dimensional Ising lattice is considered. The entropy at fixed nonuniform bond and field energies is written down as a functional of singlet and pair spin expectations, in terms of which bond and field energies are then expressed. The solution is reformulated in terms of effective fields which, in a spin-glass ensemble, are distributed as in a Markov chain. This result, and the corresponding free energy, shows that the effective field approximation previously used is exact for such systems, an assertion which extends to Cayley trees.

Original languageEnglish (US)
Pages (from-to)2561-2562
Number of pages2
JournalJournal of Mathematical Physics
Volume32
Issue number9
StatePublished - 1991

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Spin glass
Spin Glass
Ising
spin glass
Markov chains
Approximation
approximation
Markov processes
Free energy
Entropy
free energy
entropy
Cayley Tree
energy
Energy
Assertion
Free Energy
Markov chain
Ensemble

ASJC Scopus subject areas

  • Organic Chemistry

Cite this

The effective field approximation for Ising spin glasses on simply connected lattices. / Zhang, Guihua; Percus, Jerome.

In: Journal of Mathematical Physics, Vol. 32, No. 9, 1991, p. 2561-2562.

Research output: Contribution to journalArticle

Zhang, Guihua ; Percus, Jerome. / The effective field approximation for Ising spin glasses on simply connected lattices. In: Journal of Mathematical Physics. 1991 ; Vol. 32, No. 9. pp. 2561-2562.
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