Addendum to "Renormalization-group verification of crossover with respect to the lattice anisotropy parameter": Systems with first- and second-neighbor interactions

Our recently published renormalization-group treatment of the crossover phenomenon for systems with lattice anisotropy is generalized to isotropic spin systems with competing first- and second-nearest-neighbor interactions, $J_1$ and $J_2$. We find that scaling with respect to $R\equiv \frac{J_1}{J_2}$ is valid about $R=0\mathrm{}$; moreover, the crossover exponent is found to be the same as the susceptibility exponent. These results are interesting because the critical-point exponents at $R=0\mathrm{}$ and $R>\mathrm{}0\mathrm{}$ should be the same (from universality considerations). Series-expansion analysis confirms this surprising result.