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.

• Received 14 January 2009

DOI:https://doi.org/10.1103/PhysRevE.80.011103