the pinning and fluctuation strengths become complicated \[46\]. Hence, eq.(2.27) should be seen as a lower limit of the expected lower critical point. In any case, the resistivities in $B
< B_{\rm lcp}^{(p)}$ are expected to vanish continuously at the second order VG transition, and the [*thermal*]{} first order transition should not occur in these low fields where $B_m(T)$ lies in the glass phase. It is important to note that, as clear from the above discussion, a lower critical point is not due to an enhancement of pinning effect accompanying a lowering of the field: A lower critical point was observed in a couple of experiments \[7-9\] in tesla range of YBCO clean samples where the type II limit neglecting fluctuations of flux density is safely valid. It is theoretically difficult to expect a pinning-enhancement accompanying a field-lowering in type II limit. Actually, for this reason, the appearance of a lower critical point was not predicted from treatments based on the vortex elasticity.

As a test of the present explanation \[17,24\] on the existence of the vortex slush regime and of $B_{\rm lcp}$, it is interesting to compare the above results with the oxygen-deficiency dependence \[9\] of YBCO phase diagram. 