Effective spin-$\frac{1}{2}$ description of transverse-field-induced random fields in dipolar spin glasses with strong single-ion anisotropy
S. M. A. Tabei, F. Vernay, and M. J. P. Gingras

We present analytical and numerical evidence for the validity of an effective $S_{\rm eff}=\frac{1}{2}$ approach to the description of random field generation in $S\geq1,$ and especially for an $S=1$, dipolar spin glass models with strong uniaxial Ising anisotropy and subject to weak external magnetic field $B_x$ transverse to the Ising direction. Explicitly $B_x-$dependent random fields are shown to naturally emerge in the effective low-energy description of a microscopic $S=1$ toy model. We discuss our results in relation to recent theoretical studies pertaining to the topic of $B_x-$induced random fields in the LiHo$_x$Y$_{1-x}$F$_4$ magnetic materials with the Ho$^{3+}$ Ising moments subject to a transverse field. We show that the $S_{\rm eff}=\frac{1}{2}$ approach is able to capture both the qualitative and {\it quantitative} aspects of the physics at small $B_x$, giving results that agree with those obtained using conventional second order perturbation theory.

© 2008 The American Physical Society.