Specific-Heat Scaling Functions for Ising and Heisenberg Models and Comparison with Experiments on Nickel

Abstract

We calculate the scaled constant-magnetization and constant magnetic field specific heats $\frac{\left[C_M\right(\epsilon ,M)-C_M(\epsilon ,0\left)\right]}{M^{-\frac{\alpha }{\beta }}}$ and $\frac{\left[C_H\right(\epsilon ,H)-C_H(\epsilon ,0\left)\right]}{H^{-\frac{\alpha }{\beta \delta }}}$ as functions of the scaled variable $x\equiv \frac{\epsilon }{M^{\frac{1}{\beta }}}$ and $y\equiv \frac{\epsilon }{H^{\frac{1}{\beta \delta }}}$, respectively [where $\epsilon \equiv \frac{(T-T_c)}{T_c}$ and $T_c$ is the critical temperature],for the spin-½ Ising model (bcc lattice) and the spin-½, $\infty$ Heisenberg models (fcc lattice). Our calculations are based on previously calculated scaling functions for the $M(H,T)\mathrm{}$ equation of state. We also calculate the amplitudes of the zero-field specific heat for $T>\mathrm{}{T}_c$ and $T<\mathrm{}{T}_c$. Thus, we obtain the functions $C_M(\epsilon ,M)$ and $C_H(\epsilon ,H)$, though for the Heisenberg models we cannot obtain the finite nonzero constant $C_M\mathrm{}(0,0)=C_H\mathrm{}(0,0)\mathrm{}$. We compare our calculated functions with the data of Connelly, Loomis, and Mapother on nickel.