Induced-moment singlet-triplet model: Relationship between the ground-state moment and the critical temperature

Using the critical temperatures estimated by the high-temperature-series-expansion (HTSE) technique and the ground-state moment calculated in the constant-coupling approximation (CCA) we show a plot of the latter versus the former. An excellent agreement is found between our prediction and the experimental observations on ${\mathrm{Pr}}_3$Tl under a hydrostatic pressure and perhaps on ${\mathrm{Pr}}_{3-x}{\mathrm{La}}_x\mathrm{Tl}$. We also show that while the values of the critical temperatures in the CCA are generally much improved, the ground-state moment versus critical-temperature behavior predicted in CCA is as poor as that in the mean-field approximation. We emphasize that the correct behavior of the variation of $T_c$ with the crystal-field to the exchange-interaction ratio near the critical value of this ratio is the decisive factor in explaining the experimental observations.