The specific heat, the energy density and the thermodynamic Casimir force in the neighbourhood of the lambda-transition

Understand

We discuss the relation of the specific heat, the energy density and the thermodynamic Casimir effect in the case of thin films in the three dimensional XY universality class.

• The finite size scaling function $\theta(x)$ of the thermodynamic Casimir force can be expressed in terms of the scaling functions h'(x) and h(x) of the excess energy density and the excess free energy density.
• A priori these quantities depend on the reduced temperature t and the thickness L_0 of the film.
• However finite size scaling theory predicts that the scaling functions depend only on the combination x=t [L_0/\xi_0]^{1/\nu}, where \nu is the critical exponent and $\xi_0$ the amplitude of the correlation length.