Temperature chaos in a replica symmetry broken spin glass model - A hierarchical model with temperature chaos

– Temperature chaos is an extreme sensitivity of the equilibrium state to a change of temperature. It arises in several disordered systems that are described by the so called scaling theory of spin glasses, while it seems to be absent in mean field models. We consider a model spin glass on a tree and show that although it has mean field behavior with replica symmetry breaking, it manifestly has " strong " temperature chaos. We also show why chaos appears only very slowly with system size. Introduction. – The fragility of the equilibrium state to an infinitesimal change of temperature is commonly referred to as " temperature chaos " [1]. Having such fragility away from a phase transition point probably requires the system to be frustrated, but whether temperature chaos actually arises in generic frustrated systems is still subject to controversy. In the context of spin glasses [2, 3], temperature chaos is shown to be present for models on Migdal-Kadanoff lattices [4, 5]. Furthermore, the standard scaling theories [1, 6, 7] suggest that this is a general property of glassy systems; in support of this, the Directed Polymer in a Random Medium [8] (DPRM), which is well described by the (spin glass) scaling theories , is shown to have temperature chaos [9, 10]. On the other hand, the Random Energy Model [11] has no temperature chaos [12], and what happens in the Sherrington-Kirkpatrick (SK) mean-field model of spin glasses is still unclear. A replica calculation for the SK model suggests the presence of temperature chaos [12], but the numerics indicate no chaos or only very weak chaos [13–15]. Furthermore, a more recent calculation by Rizzo [16] shows that temperature chaos is absent in perturbation theory about the critical temperature T c to the orders computed. To clarify this question of temperature chaos in mean-field spin glasses, in this paper we study a specific mean-field-like model. By determining the probability density of overlaps for two real replicas at two different temperatures, we show that this model has temperature chaos even though it has a mean field behavior with replica symmetry breaking. Our quantitative study also gives a coherent picture of chaos and suggests why chaos is so weak in general.