The full H-T phase diagram in the nematic superconductor FeSe is mapped out using specific-heat and thermal-expansion measurements down to 0.7 K and up to 30 T for both field directions. A clear thermodynamic signal of an underlying vortex-melting transition is found in both datasets and could be followed down to low temperatures. The existence of significant Gaussian thermal superconducting fluctuations is demonstrated by a scaling analysis, which also yields the mean-field upper critical field Hc2(T). For both field orientations, Hc2(T) shows Pauli-limiting behavior. Whereas the temperature dependence of the vortex-melting line is well described by the model of Houghton et al., Phys. Rev. B 40, 6763 (1989) down to the lowest temperatures for H $perp$ FeSe layers, the vortex-melting line exhibits an unusual behavior for fields parallel to the planes, where the Pauli limitation is much stronger. Here, the vortex-melting anomaly is only observed down to T*= 2-3 K, and then merges with the Hc2(T) line as predicted by Adachi and Ikeda, Phys. Rev. B 68 184510 (2003). Below T*, Hc2(T) also exhibits a slight upturn possibly related to the occurence of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state.
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