Universal trend in the heat capacity of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ near ${\mathit{T}}_{\mathit{c}}$(x)

The reduction in transition temperature that occurs as oxygen is removed from ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ is accompanied by a rapid decrease in the size of the heat-capacity anomaly at ${\mathit{T}}_{\mathit{c}}$. We treat the fluctuation effects in the context of XY-like behavior and demonstrate that their dependence on the transition temperature agrees in detail with a relationship between ${\mathit{T}}_{\mathit{c}}$ and the hole concentration proposed by Schneider and Keller. Further, we show that this empirical relationship can be understood by combining scaling arguments with the nearly antiferromagnetic Fermi-liquid model of Monthoux and Pines.