Weighted averages of TAP solutions and Parisi's q(x)
- 20 February 1984
- journal article
- Published by IOP Publishing in Journal of Physics C: Solid State Physics
- Vol. 17 (5) , L155-L160
- https://doi.org/10.1088/0022-3719/17/5/006
Abstract
Generating functions of the form Z(u)= Sigma s exp(u beta Fs) are considered, where the sum is over solutions of the Thouless-Anderson-Palmer (TAP) equations for the Sherrington-Kirkpatrick spin glass model and Fs is the free energy of solution s. It is shown that the weight function exp(u beta Fs)/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)=qP( mod u mod x) for mod u mod xp(x) is the Parisi function for the canonical weight (u=-1) and x is the 'break point' in the Parisi function.Keywords
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