HUBBARD-MODEL - FIELD-THEORY AND CRITICAL PHENOMENA

In this work we use field-theoretic and renormalization-group methods to study the finite-temperature ferromagnetic phase transition in the three-dimensional Hubbard model. We show that the nature of the ferrom agnetic transition may strongly depend on the constraint imposed on th e system. For example, if the system is allowed to exchange particles with a reservoir, the stability criterion for the occurrence of a cont inuous phase transition can be calculated using the mean-field approxi mation. On the other hand, if the total charge is conserved and charge - and spin-density fluctuations are considered in the theory, a differ ent criterion, quite distinct from the mean-field one, is found, resul ting in a fluctuation-induced renormalized Heisenberg tricritical poin t. The tricritical behavior is studied by calculating the one-loop ren ormalized free energy and using scaling analysis to determine the tric ritical exponents. Finally, the exact solution of the model in the sph erical limit and near the ferromagnetic transition is presented, in wh ich case no fluctuation-induced tricritical point is found.