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 ferromagnetic transition may strongly depend on the constraint imposed on the system. For example, if the system is allowed to exchange particles with a reservoir, the stability criterion for the occurrence of a continuous phase transition can be calculated using the mean-field approximation. On the other hand, if the total charge is conserved and charge- and spin-density fluctuations are considered in the theory, a different criterion, quite distinct from the mean-field one, is found, resulting in a fluctuation-induced renormalized Heisenberg tricritical point. The tricritical behavior is studied by calculating the one-loop renormalized free energy and using scaling analysis to determine the tricritical exponents. Finally, the exact solution of the model in the spherical limit and near the ferromagnetic transition is presented, in which case no fluctuation-induced tricritical point is found.