We have measured the specific heat of an S=1/2 antiferromagnetic alternating Heisenberg chain pentafulorophenyl nitronyl nitroxide under magnetic fields up to H>H_C2. This compound has the field-induced magnetic ordered (FIMO) phase between H_C1 and H_C2. Characteristic behaviors are observed depending on the magnetic field up to above H_C2 outside of the H-T boundary for the FIMO. Temperature and field dependence of the specific heat are qualitatively in good agreement with the theoretical calculation on an S=1/2 two-leg ladder. [Wang et al. Phys. Rev. Lett 84 5399 (2000)] This agreement suggests that the observed behaviors are related with the low-energy excitation in the Tomonaga-Luttinger liquid.
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