Scaling Theory for Finite-Size Effects in the Critical Region

Abstract

Critical phenomena in films of finite thickness are considered. A detailed scaling theory, with allowance for distinct exponents $\ensuremath{\lambda}$ and $\ensuremath{\theta}=\frac{1}{\ensuremath{\nu}}$ for the critical-point shift and rounding, respectively, is confirmed by exact calculations on $d$-dimensional ferromagnetic spherical models and ideal Bose fluids with various boundary conditions. Isingmodel results and existing data on real helium films are consistent with the theory.