Weighted averages of TAP solutions and Parisi's q(x)
A J Bray; M A Moore; A P Young; A J Bray; Dept. of Theoretical Phys., Univ. of Manchester, Manchester, UK; M A Moore; Dept. of Theoretical Phys., Univ. of Manchester, Manchester, UK; A P Young; Dept. of Theoretical Phys., Univ. of Manchester, Manchester, UK
Журнал:
Journal of Physics C: Solid State Physics
Дата:
1984-02-20
Аннотация:
Generating functions of the form Z(u)= Sigma <sub>s</sub> exp(u beta F<sub>s</sub>) are considered, where the sum is over solutions of the Thouless-Anderson-Palmer (TAP) equations for the Sherrington-Kirkpatrick spin glass model and F<sub>s</sub> is the free energy of solution s. It is shown that the weight function exp(u beta F<sub>s</sub>)/Z(u) projects out solutions of the lowest free energy for all u less than a critical value. The associated Parisi order parameter function q(x) has the scaling form q(x)=q<sub>P</sub>( mod u mod x) for mod u mod x<x, where q<sub>p</sub>(x) is the Parisi function for the canonical weight (u=-1) and x is the 'break point' in the Parisi function.
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