Double-Power Scaling Functions near Tricritical Points

We introduce invariants of the scaling equation about the tricritical point. Using these invariants, a modified version of the scaling hypothesis about the three critical lines meeting at the tricritical point is presented. From it we demonstrate that the thermodynamic equation of state near a tricritical point and near a critical line may be expressed as double-power scaling functions. These imply that experimental data should collapse from a volume onto a line (i.e., by two dimensions). This behavior is in contrast to ordinary "single-power" scaling functions, which predict data collapsing from a volume onto a surface or from a surface onto a line (i.e., by one dimension).