Evidence for 3D-xy critical properties in underdoped YBa2Cu3O7+x
  We perform a detailed analysis of the irreversible magnetization data of Salem-Sugui et al. and Babis et al. of underdoped and optimally doped YBa2Cu3O7+x single crystals. Near the zero field transition temperature we observe extended consistency with the properties of the 3D-xy universality class, even though the attained critical regime is limited by an inhomogeneity induced finite size effect. Nevertheless, as Tc falls from 93.5 to 41.5 K the critical amplitude of the in-plane correlation length gsiab0, the anisotropy amma=gsiab0/gsic0 and the critical amplitude of the in-plane penetration depth Lamdaab0 increase substantially, while the critical amplitude of the c-axis correlation length gsic0 does not change much. As a consequence, the correlation volume Vcorr increases and the ritical amplitude of the specific heat singularity A decreases dramatically, while the rise of gsiab0 reflects the behavior of the zero temperature counterpart. Conversely, although gsiab0 and lamdaab0 increase with reduced Tc, the Ginzburg-Landau parameter decreases substantially and YBa2Cu3O7+x crosses over from an extreme to a weak type-II superconductor. 
T. Schneider