Thermodynamic construction of a one-step replica-symmetry-breaking solution in finite-connectivity spin glasses.
A one-step replica-symmetry-breaking solution for finite-connectivity spin-glass models with K body interaction is constructed at finite temperature using the replica method and thermodynamic constraints. In the absence of external fields, this construction provides a general extension of replica symmetric solution at finite replica number to one-step replica-symmetry-breaking solution. It is found that this result is formally equivalent to that of the one-step replica-symmetry-breaking cavity method. To confirm the validity of the obtained solution, Monte Carlo simulations are performed for K=2 and 3. The thermodynamic quantities of the Monte Carlo results extrapolated to a large-size limit are consistent with those estimated by our solution for K=2 at all simulated temperatures and for K=3 except near the transition temperature.
Nakajima
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T
Department of Basic Science, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan. tetsuya@huku.c.u-tokyo.ac.jp
Hukushima
K
K