  We study the problem of chaos in temperature in some mean-field spin-glass
models by means of a replica computation over a model of coupled systems. We
propose a set of solutions of the saddle point equations which are
intrinsically non-chaotic and solve a general problem regarding the consistency
of their structure. These solutions are relevant in the case of uncoupled
systems too, therefore they imply a non-trivial overlap distribution
$P(q_{T1T2})$ between systems at different temperatures. The existence of such
solutions is checked to fifth order in an expansion near the critical
temperature through highly non-trivial cancellations, while it is proved that a
dangerous set of such cancellations holds exactly at all orders in the
Sherrington-Kirkpatrick (SK) model. The SK model with soft-spin distribution is
also considered obtaining analogous results. Previous analytical results are
discussed.
