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

Guihua Zhang, J. K. Percus

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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
Issue number9
StatePublished - Jan 1 1991


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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