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Replica symmetry breaking solution for the fermionic Ising spin-glass and the Ghatak-Sherrington model

H Feldmann and R Oppermann

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We solve the fermionic version of the Ising spin glass for arbitrary filling µ and temperature T taking into account replica symmetry breaking. Using a simple exact mapping from µ to the anisotropy parameter D , we also obtain the solution of the S = 1 Sherrington-Kirkpatrick model. An analytic expression for T = 0 gives an improved critical value for the first-order phase transition. We revisit the question of stability against replica-diagonal fluctuations and find that the appearance of complex eigenvalues of the Almeida-Thouless matrix is not an artefact of the replica-symmetric approximation.


PACS

05.50.+q Lattice theory and statistics (Ising, Potts, etc.)

02.10.Ud Linear algebra

05.70.Fh Phase transitions: general studies

MSC

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

82D30 Random media, disordered materials (including liquid crystals and spin glasses)

82B26 Phase transitions (general)

15A18 Eigenvalues, singular values, and eigenvectors

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 7 (25 February 2000)

Received 27 September 1999



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