| 概要 | We consider a modification of the generalized random energy model (GREM) in spin glass theory, which can be fully analyzed in the whole temperature regime, and which has some of the key properties predicted in spin glass theory, which are lacking in the GREM case. The model is obtained by a non-linear transformation of a macroscopically large family of cavity variables whose covariances are given in a hierarchical way. In contrast to the GREM itself, the model has a rich asymptotic behavior. The free energy is given by a formula which closely resembles the Parisi formula for the SK model. The limiting ultrametric structure depends in a complicated way on the temperature parameter. Also, in contrast to the GREM, the model has the chaos property (in temperature). |