Magnetic phase diagram of the half-filled Hubbard model for a simple cubic lattice

We have calculated the $U-T$ phase diagram of the half-filled simple-cubic Hubbard model ($U$: interaction, $T$: temperature) by making use of the two interpolation theories, the single-site spin-fluctuation (SSF) theory proposed by Hubbard and Hasegawa and the Gutzwiller-type variational approach (VA) by Kakehashi and Fulde. The results are compared with those of the recent Monte Carlo (MC) calculations made by Hirsch for a three-dimensional 4×4×4 lattice. The Néel temperatures $T_N$ calculated with the MC method are about 70% higher than those calculated with the mean-field-type theories of the SSF and VA though the $U$ dependence of the amplitudes of the local moments and charge fluctuations agrees well with our results. This suggests an overestimation of $T_N$ up to 100% in Hirsch's calculations, whose conceivable origins are discussed. We present also the result of the internal energy as a function of $T$ and $U$ calculated using the SSF and VA.