26 FIG. 24: (Color online) Phase diagram for the classical Heisenberg antiferromagnet on a pyrochlore lattice, Eq. (1), in applied magnetic field h = 0 , with additional biquadratic interactions b = 0 . 6 . The transition temperature T N associated with the E –symmetry long– range order vanishes as the strength of ferromagnetic third–neighbor interactions J$_{3}$ → 0 , as determined by Monte Carlo simulation. A phase exhibiting nematic order exists above T N up to a T Q ∼ b .