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

Abstract

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 $|\mathbf{k}{|}^{\ensuremath{-}3}$ 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.