A method for estimating the entropy $S$ from a Monte Carlo simulation, suggested previously by the author, is applied to the fcc Ising antiferromagnet with nearest-neighbor interactions and external magnetic field $h$. The estimated accuracy for $S$ is 0.01% to 0.5%, which is, at least, 1 order of magnitude higher than has been obtained with thermodynamic integration by Binder. Comparison of the free-energy results for the coexisting ordered and disordered phases enables us to determine with high accuracy the first-order transition points and the discontinuities in the thermodynamic functions. For the residual ground-state entropies per spin $\frac{S\left(0\right)\mathrm{}}{k_B}$ at the critical fields $\frac{h_c}{J}=12\mathrm{}$ and 4, we obtain 0.249 89(2) [=0.369 51(3)ln2] and 0.239(1) [=0.345(1)ln2], respectively. The first result is significantly larger than the theoretical upper bound, ${\sigma }_u^{\prime }=0.2398\mathrm{}$ (=0.3460ln2), conjectured by Hadjuković and Milošević. Our results are also significantly larger than Binder's result, ~⅓ ln2, obtained for both critical fields.

• Received 15 December 1983

DOI:https://doi.org/10.1103/PhysRevB.30.2866