Power-law correlations and orientational glass in random-field Heisenberg models

Monte Carlo simulations have been used to study a discretized Heisenberg ferromagnet (FM) in a random field on simple cubic lattices. The spin variable on each site is chosen from the 12 [110] directions. The random field has infinite strength and a random direction on a fraction x of the sites of the lattice, and is zero on the remaining sites. For x = 0 there are two phase transitions. At low temperature there is a [110] FM phase, and at intermediate temperature there is a [111] FM phase. For x > 0 there is an intermediate phase between the paramagnet and the ferromagnet, which is characterized by a \ k \-3 decay of two-spin correlations, but no true FM order. The [111] FM phase becomes unstable at a small value of x. At x=1/8 the [110] FM has disappeared, but the power-law correlated phase survives.