Abstract:
We study the Sherrington-Kirkpatrick model of a spin glass in order to identify the origin of the order parameters needed for a consistent description of the spin glass phase. We use the thermodynamic approach of Thouless, Anderson, and Palmer for the evaluation of thermal fluctuations for one configuration of spin couplings. We demonstrate that due to degeneracy in free energy the TAP states become unstable in the spin-glass phase. To stabilize the equilibrium state we have to lift the degeneracy and introduce new homogeneous order parameters. We show that these parameters are closely related to the parameters of the Parisi replica-symmetry breaking solution. The new mean-field equations are resolved for the homogeneous order parameters near the critical point iteratively and an explicit dependence on the number of iterations (hierarchies) toward the full exact solution is presented.