Within the framework of the $\epsilon$ expansion, we establish a symmetry criterion allowing us to predict if a phase transition is driven first order by the fluctuations. It is expressed in the form of group-theoretical conditions imposed on the Hamiltonian symmetry. In particular, we specify a sufficient condition for the lack of a stable-fixed-point Hamiltonian. The effectiveness of this condition is illustrated by its application to Hamiltonians based on four-component order parameters.

• Received 2 January 1985

DOI:https://doi.org/10.1103/PhysRevLett.54.1832