Ising-Model Critical Indices below the Critical Temperature

We review the estimates for the critical indices of the Ising model below $T_C$ and conclude (for 3 dimensions): ${\alpha }^{\prime }=0.066_{-0.04\mathrm{}}^{}{}_{}{}^{+0.16\mathrm{}}$, $\beta =0.312_{-0.005\mathrm{}}^{}{}_{}{}^{+0.002\mathrm{}}$, ${\gamma }^{\prime }=1.310_{-0.05\mathrm{}}^{}{}_{}{}^{+0.04\mathrm{}}$ for the specific heat, magnetization, and magnetic susceptibility, respectively. For 2 dimensions, we estimate ${\gamma }^{\prime }=1.75_{-0.00\mathrm{}}^{}{}_{}{}^{+0.01\mathrm{}}$. In order to explain previous estimates of ${\alpha }^{\prime }=0\mathrm{}$, we point out that a low power can, in practice, look deceptively like a logarithm. Finally, we discuss the behavior of the specific heat at constant magnetization.