Power-law correlated phase in random-field XY models and randomly pinned charge-density waves

Monte Carlo simulations have been used to study the Z(N) ferromagnet in a random field on simple cubic lattices for N=6 and N=12. The random field is chosen to have infinite strength and random direction on a fraction x of the sites of the lattice, and to be zero on the remaining sites. For N=6 and x=1/16 there are two phase transitions. At low temperature there is a ferromagnetic phase, which is stabilized by the sixfold nonrandom anisotropy. The intermediate temperature phase is characterized by a \k\(-3) decay of two-spin correlations, but no true ferromagnetic order. At the transition between the power-law correlated phase and the paramagnetic phase the magnetic susceptibility diverges, and the two-spin correlations decay approximately as \k\(-2.87). There is no evidence for a latent heat at either transition, but the magnetization seems to disappear discontinuously. For N=6 and x=1/8 the correlation length never exceeds 12, and the paramagnetic phase goes directly into the ferromagnetic phase; the two-spin correlation function is peaked at small \k\, but the only divergence is the ferromagnetic delta function at \k\=0. Results in the paramagnetic and power-law correlated phases for N=12 are essentially identical to those for N=6, so the power-law correlated phase should exist in the limit N-->infinity. The ferromagnetic phase terminates near x=1/6 for N=6, but the limit of ferromagnetic stability for N=12 is less than x=1/16.