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Renormalisation-group theory of the phase transition in ultrametric spin glasses

Spin-glass systems possessing the hierarchical tree-like structure of thermodynamically relevant metastable states are considered. A renormalisation-group scheme for the calculation of the partition function is proposed, and a systematic method for the calculation of the renormalised Hamiltonian with increasing scale in the space of states is derived. The renormalisation-group equations for the parameters of the renormalised Hamiltonian (which contain all powers of the spin variables) are obtained. For the model with infinite-range Gaussian interactions, the well known results for the phase transition are recovered.