An exact result for the 1D random Ising model in a transverse field

It is shown exactly that for an N-site cyclic chain with hamiltonian H = − Σ N i=1 ( γ i S x i + J i S z i S z i S z i+1 ), the gap in the excitation spectrum goes to zero when N → ∞ at the “critical point” given by the relation Π N i=1 Γ i = Π N i=1 J i .

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Bibliographic Details
Published in:Physics letters. A 1979-01, Vol.72 (3), p.245-246
Main Author: Pfeuty, P.
Format: Article
Language:English
Subjects:
Condensed Matter
Physics
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Summary:It is shown exactly that for an N-site cyclic chain with hamiltonian H = − Σ N i=1 ( γ i S x i + J i S z i S z i S z i+1 ), the gap in the excitation spectrum goes to zero when N → ∞ at the “critical point” given by the relation Π N i=1 Γ i = Π N i=1 J i .
ISSN:0375-9601
1873-2429
DOI:10.1016/0375-9601(79)90017-3