  Cu$_{0.5}$Co$_{0.5}$Cl$_{2}$-FeCl$_{3}$ graphite intercalation compound is a
three-dimensional short-range Ising spin glass with a spin freezing temperature
$T_{c}$ ($= 3.92 \pm 0.11$ K). The stability of the spin glass phase in the
presence of a magnetic field $H$ is examined from (i) the spin freezing
temperature $T_{f}(\omega,H)$ at which the differential field-cooled (FC)
susceptibility $\partial M_{FC}(T,H)/\partial H$ coincides with the dispersion
$\chi^{\prime}(\omega,T,H=0)$ with the angular frequency $\omega$, and (ii) the
time dependence of zero-field cooled (ZFC) susceptibility $\chi_{ZFC}$ after a
ZFC aging protocol with a wait time $t_{W}$ ($= 1.0 \times 10^{4}$). The
relaxation rate $S(t)$ (= d$\chi_{ZFC}$/d$\ln t$) exhibits a local maximum at a
characteristic time $t_{cr}$, reflecting non-equilibrium aging dynamics. The
peak time $t_{cr}(T,H)$ decreases with increasing $H$ at the fixed temperature
$T$ (2.9 K $\leq T<T_{c}$). The spin freezing temperature $T_{f}(\omega,H)$
provides evidence for the instability of the spin glass phase in thermal
equilibrium in a finite magnetic field. Both $t_{cr}(T,H)$ and
$T_{f}(\omega,H)$ exhibit certain scaling behavior predicted from the droplet
picture, suggesting a dynamic crossover from SG dynamics to paramagnetic
behavior in the presence of $H$.
