Abstract
The finite temperature dynamics of the Dyson hierarchical classical spins models is studied via real-space renormalization rules concerning the couplings and the relaxation times. For the ferromagnetic model involving long-ranged coupling in the region where there exists a non-mean-field-like thermal ferromagnetic–paramagnetic transition, the RG flows are explicitly solved: the characteristic relaxation time follows the critical power-law at the phase transition and the activated law with in the ferromagnetic phase. For the spin-glass model involving random long-ranged couplings of variance in the region where there exists a non-mean-field-like thermal spin-glass–paramagnetic transition, the coupled RG flows of the couplings and of the relaxation times are studied numerically: the relaxation time follows some power-law at criticality and the activated law in the spin-glass phase with the dynamical exponent coinciding with the droplet exponent governing the flow of the couplings .
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