Title: Dynamic scaling analysis of the long-range RKKY Ising spin glass Dy$_{x}$Y$_{1-x}$Ru$_{2}$Si$_{2}$,
Abstract: Dynamic scaling analyses of linear and nonlinear ac susceptibilities in a
model magnet of the long-rang RKKY Ising spin glass (SG)
Dy$_{x}$Y$_{1-x}$Ru$_{2}$Si$_{2}$ were examined. The obtained set of the
critical exponents, $\gamma$ $\sim$ 1, $\beta$ $\sim$ 1, $\delta$ $\sim$ 2, and
$z\nu$ $\sim$ 3.4, indicates the SG phase transition belongs to a different
universality class from either the canonical (Heisenberg) or the short-range
Ising SGs. The analyses also reveal a finite-temperature SG transition with the
same critical exponents under a magnetic field and the phase transition line
$T_{\mbox{g}}(H)$ described by $T_{\mbox{g}}(H)$ $=$
$T_{\mbox{g}}(0)(1-AH^{2/\phi})$ with $\phi$ $\sim$ 2. The crossover exponent
$\phi$ obeys the scaling relation $\phi$ $=$ $\gamma + \beta$ within the margin
of errors. These results strongly suggest the spontaneous
replica-symmetry-breaking (RSB) with a {\it non- or marginal-mean-field
universality class} in the long-range RKKY Ising SG.