Crossover in anisotropic Pottsφ3field theory with quadratic symmetry breaking

A continuous ${\phi }^3$ field theory with quadratic symmetry breaking and isotropic trilinear interaction $g_0 \Sigma d_{\mathrm{ijk}}{\phi }_i{\phi }_j{\phi }_k$ is studied, to one-loop order in dimension $d=6-\epsilon$, for an anisotropic ($n+1\mathrm{}$)-state Potts model. Effective critical exponents for the crossover induced by quadratic symmetry breaking are calculated, and the results, in the limit $n=0\mathrm{}$, are applicable to the thermally driven crossover in random bond-diluted ferromagnets near the percolation threshold. The limitation of a single renormalized $g$ is explicitly pointed out.