We have measured the specific heat and magnetization {it versus} temperature in a single crystal sample of superconducting La$_{2}$CuO$_{4.11}$ and in a sample of the same material after removing the excess oxygen, in magnetic fields up to 15 T. Using the deoxygenated sample to subtract the phonon contribution, we find a broad peak in the specific heat, centered at 50 K. This excess specific heat is attributed to fluctuations of the Cu spins possibly enhanced by an interplay with the charge degrees of freedom, and appears to be independent of magnetic field, up to 15 T. Near the superconducting transition $T_{c}$($H$=0)= 43 K, we find a sharp feature that is strongly suppressed when the magnetic field is applied parallel to the crystallographic c-axis. A model for 3D vortex fluctuations is used to scale magnetization measured at several magnetic fields. When the magnetic field is applied perpendicular to the c-axis, the only observed effect is a slight shift in the superconducting transition temperature.
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