University in Analytic Corrections to Scaling for Planar Ising Models

It is argued that the leading corrections to scaling for planar Ising models, which occur as analytic factors, arise from the quadratic terms of the nonlinear thermal and ordering fields (rather than from irrelevant variables). This yields ${{\alpha }_{\mathrm{eff}}}^{\prime }+2\mathrm{}{\beta }_{\mathrm{eff}}+{{\gamma }_{\mathrm{eff}}}^{\prime }=2\mathrm{}$ for the effective critical exponents, with $\mathrm{no}$ leading corrections, and is confirmed by exact square-lattice results for arbitrary anisotropy $\frac{J_2}{J_1}$. For isotropic lattices the ratios of correction amplitudes and quadratic nonlinear-field terms appear universal.