Charge-density-wave order parameter of the Falicov-Kimball model in infinite dimensions

In the large-$U$ limit, the Falicov-Kimball model maps onto an effective Ising model, with an order parameter described by a BCS-like mean-field theory in infinite dimensions. In the small-$U$ limit, van Dongen and Vollhardt showed that the order parameter assumes a strange non-BCS-like shape with a sharp reduction near $T\approx T_c/2.\mathrm{}$ Here we numerically investigate the crossover between these two regimes and qualitatively determine the order parameter for a variety of different values of U. We find the overall behavior of the order parameter as a function of temperature to be quite anomalous.