Dyson's equations for the (Ising) spin-glass

C. De Dominicis, I. Kondor, T. Temesvari

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

A complex problem is solved here; we show how to write Dyson's equations for the (Ising) spin-glass that relate the propagator G to the mass operator M. In other words we are able to reduce the inversion of an ultrametric matrix M to the solution of a Dyson's equation in all sectors (for the replicon sector the result had already been derived). It turns out that what renders the problem tractable is using, instead of the components of G (or M), an object called here the 'kernel' from which one can deduce the components themselves after dressing it with ultrametric weights and summing over eigenvalue indices with their appropriate multiplicity. Dyson's equations are then established as stationarity equations of tr 1n M - tr GM, where the kinetic terms are incorporated in M. At each stage we illustrate the calculation by providing explicit answers for the bare system (mean field in M). In particular the introduction of the 'kernel' allows us to construct the bare propagator for a Lagrangean where one retains all quartic invariants. The case of the system in a magnetic field is also treated.

Original languageEnglish
Pages (from-to)1287-1308
Number of pages22
JournalJournal de physique. III
Volume4
Issue number9
Publication statusPublished - Sep 1994

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Spin glass
spin glass
Magnetic fields
Kinetics
sectors
propagation
eigenvalues
inversions
operators
kinetics
matrices
magnetic fields

ASJC Scopus subject areas

  • Engineering(all)

Cite this

De Dominicis, C., Kondor, I., & Temesvari, T. (1994). Dyson's equations for the (Ising) spin-glass. Journal de physique. III, 4(9), 1287-1308.

Dyson's equations for the (Ising) spin-glass. / De Dominicis, C.; Kondor, I.; Temesvari, T.

In: Journal de physique. III, Vol. 4, No. 9, 09.1994, p. 1287-1308.

Research output: Contribution to journalArticle

De Dominicis, C, Kondor, I & Temesvari, T 1994, 'Dyson's equations for the (Ising) spin-glass', Journal de physique. III, vol. 4, no. 9, pp. 1287-1308.
De Dominicis C, Kondor I, Temesvari T. Dyson's equations for the (Ising) spin-glass. Journal de physique. III. 1994 Sep;4(9):1287-1308.
De Dominicis, C. ; Kondor, I. ; Temesvari, T. / Dyson's equations for the (Ising) spin-glass. In: Journal de physique. III. 1994 ; Vol. 4, No. 9. pp. 1287-1308.
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