Field theory with Φ4 and Φ6 self-interaction.

Abstract

A theory for a scalar field with a potential corresponding to three wells is analyzed. Use is made of the lattice approximation and the block-spin renormalization-group method keeping the three lowest levels at each site. A second-order or a first-order phase transition appears according to the relative depths of the wells and the intersite coupling. The same qualitative scheme emerges from a mean-field approximation.