Universal Ratios Among Correction-to-Scaling Amplitudes on the Coexistence Curve

Abstract

Correction-to-scaling amplitudes are calculated to second order in $\ensuremath{\epsilon}=4\ensuremath{-}d$ by renormalized perturbation theory. It is shown that ratio of any two such amplitudes is universal, and that thermodynamic scaling laws among effective exponents break down beyond zeroth order in $\ensuremath{\epsilon}$. Values found are $\frac{{{a}_{\ensuremath{\xi}}}^{+}}{{{a}_{\ensuremath{\chi}}}^{+}}=0.65 (n=1, d=3) \mathrm{and} 0.63 (n=2, d=3)$ in good agreement with high-temperature series, and $\frac{{{a}_{m}}^{\ensuremath{-}}}{{{a}_{\ensuremath{\chi}}}^{+}}=0.85 (n=1, d=3)$.