Against temperature chaos in naive Thouless-Anderson-Palmer equations

We study the temperature structure of the naive TAP equations by mean of a recursion algorithm. The problem of the chaos in temperature is addressed using the notion of the temperature evolution of equilibrium states. The lowest free energy states show relevant correlations with the ground state, and a careful finite size analysis indicates that these correlations are not finite size effects, ruling out the possibility of chaos in temperature even in the thermodynamic limit. The correlations of the equilibrium states with respect to the ground state are investigated. The performance of a new heuristic algorithm for the search of ground states is also discussed.