Specific Heat of the Dilute Ising Magnet LiHo$_x$Y$_{1-x}$F$_4$

We will present specific heat results on the dilute dipolar-coupled Ising magnet LiHo$_x$Y$_{1-x}$F$_4$. This material was previously observed to change from a spin glass to an unusual ``anti-glass'' state at a Ho concentration of $x\simeq 0.045$. This state showed dynamics that are very different from those of a spin glass\footnote{S. Ghosh \emph{et al.}, Science {\bf 296}, 2195 (2002)} and also exhibited sharp features in its specific heat at around 100 and 300 mK\footnote{S. Ghosh \emph{et al.}, Nature {\bf 425}, 48 (2003).}. In contrast, our measurements of the heat capacity do not reproduce these sharp features and instead find broad curves for three concentrations (1.8\%, 4.5\% and 8.0\%). Integrating $C/T$ reveals a residual entropy $S_0$ which is 0 for 8.0\% Ho but increases with lower concentration (to $0.31R$ at 1.8\% Ho). This provides some evidence for a change to a different magnetic ground state below 8.0\% Ho and is qualitatively consistent with Monte Carlo simulations\footnote{J. Snider and C. C. Yu, Phys. Rev. B {\bf 72}, 214203 (2005).}. AC susceptibility measurements probing the dynamics of this system are currently being performed and results will be presented.