The specific heat $C(T)$ of new iron-based high-$T_c$ superconductor SmO$_{1-x}$F$_x$FeAs ($0 leq x leq 0.2$) was systematically studied. For undoped $x$ = 0 sample, a specific heat jump was observed at 130 K. This is attributed to the structural or spin-density-wave (SDW) transition, which also manifests on resistivity as a rapid drop. However, this jump disappears with slight F doping in $x$ = 0.05 sample, although the resistivity drop still exists. The specific heat $C/T$ shows clear anomaly near $T_c$ for $x$ = 0.15 and 0.20 superconducting samples. Such anomaly has been absent in LaO$_{1-x}$F$_x$FeAs. For the parent compound SmOFeAs, $C(T)$ shows a sharp peak at 4.6 K, and with electron doping in $x$ = 0.15 sample, this peak shifts to 3.7 K. It is interpreted that such a sharp peak results from the antiferromagnetic ordering of Sm$^{3+}$ ions in this system, which mimics the electron-doped high-$T_c$ cuprate Sm$_{2-x}$Ce$_x$CuO$_{4-delta}$.
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