Universal Ratios Among Correction-to-Scaling Amplitudes and Effective Critical Exponents

Abstract

Writing thermodynamic quantities near a critical point as $f_i\sim A_i{\mathrm{}\left|t\right|\mathrm{}}^{-{\lambda }_i}(1+a_i{\mathrm{}\left|t\right|\mathrm{}}^{\Delta })$, where $t=\frac{(T-T_c)}{T_c}$, we show that to leading order in $\epsilon =4-d$ one has $\frac{a_i}{a_j}=\frac{({\lambda }_i-{{\lambda }_i}^0)}{({\lambda }_j-{{\lambda }_j}^0)}$, where ${{\lambda }_i}^0$ is the mean-field value of ${\lambda }_i$. This ratio is also equal to $\frac{({\lambda }_{i, \mathrm{eff}}-{\lambda }_i)}{({\lambda }_{j, \mathrm{eff}}-{\lambda }_j)}$, where ${\lambda }_{i, \mathrm{eff}}$ is derived from a fit of data with $f_i\sim {\mathrm{}\left|t\right|\mathrm{}}^{-{\lambda }_{i, \mathrm{eff}}}$. Various experiments are analyzed and compared to these predictions.