On the critical behaviour of Dyson's quantum hierarchical models

Abstract

We study the probability distribution of the appropriately scaled square of the total spin for critical asymptotically hierarchical quantum models and show that it converges, as the number of spins tends to infinity, to the same function related to the corresponding classical systems. Thus, we exhibit explicitly a property of statistical mechanical systems which, at the critical point, does not depend whether one uses a classical or quantum mechanical description.