Phase diagram for the Ashkin-Teller model in three dimensions

High- and low-temperature series, Monte Carlo simulations, mean-field calculations, and renormalization-group ideas are used to analyze the behavior of the Ashkin-Teller model in three dimensions. The data generated by series and Monte Carlo methods in the neighborhood of the decoupling point are consistent with the renormalization-group conclusion that this system cannot show a line of continuously varying exponents. Thus the phase diagram for the $d=3\mathrm{}$ system is quite different from that in $d=2\mathrm{}$. Indeed a new phase (not seen in $d=2\mathrm{}$) is observed, one in which the system spontaneously breaks its natural symmetry between its two kinds of Ising spins. A variety of continuous transitions are observed and explained in terms of an analysis which is fully consonant with renormalization-group concepts.