Hierarchical models of spin glasses

Asymptotic hierarchical Dyson models defined by random Hamiltoniaas are considered. They can be regarded as hierarchical models of spin glasses. An interval of temperatures is found in which the probability distribution for the normalized mean spin converges weakly to a Ganssian distribution. It is also shown that for some hierarchical models of a spin glass the limiting free energy is infinite with positive probability when the coupling constant satisfies $c>2$.