Number of solutions of the TAP equations for p--spin interaction spin glasses

Details Number of solutions of the TAP equations for p--spin interaction spin glasses Number of solutions of the TAP equations for p--spin interaction spin glasses

1992-08-25

arxiv.org/abs/cond-mat/9208015v1

Physics

Condensed Matter

13 pages + 2 figures (postscript files included!), needs REVTEX

Scientific paper

10.1103/PhysRevB.46.14655

The number $\langle N_s\rangle$ of solutions of the equations of Thouless, Anderson and Palmer for p--spin interaction spin glass models is calculated. Below a critical temperature $T_c$ this number becomes exponentially large, as it is in the SK--model ($p=2$). But in contrast to this, for any $p>2$ the factor $\alpha(T)=N^{-1} \ln\langle N_s\rangle$ jumps discontinuously at $T_c(p)$, which is consistent with the discontinuity occuring within the mean--field theory for these models. For zero temperature the results obtained by Gross and M\'ezard are reproduced, and for $p\rightarrow\infty$ one gets the result for the random energy model.

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