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 6 ferromagnet in a random field on simple cubic lattices, which is a simple model for randomly pinned charge-density waves. 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 x= 1/16 there are two phase transitions. At low temperature there is a ferromagnetic phase, which is stabilized by the six-fold nonrandom anisotropy. The intermediate temperature phase is characterized by a | k | −3 decay of twospin 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 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. The ferromagnetic phase terminates near x= 1/6. PACS numbers: 71.45.Lr, 71.55.Jv, 75.10.Nr, 75.40.Mg