One step replica symmetry breaking and overlaps between two temperatures

We obtain an exact analytic expression for the average distribution, in thermodynamic limit, of overlaps between two copies same random energy model (REM) at different temperatures. quantify non-self averaging effects and provide approach to computation fluctuations distribution limit. show that overlap probabilities satisfy recurrence relations generalise Ghirlanda-Guerra identities also analyse temperature REM using replica method. The expressions as form. how a generalisation Parisi's symmetry breaking ansatz is consistent with our expressions. A crucial aspect this we must allow block sizes even This contrasts single case where extremal condition leads fixed size Finally, generalised Parisi general they may have negative variance.