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 $\lambda$ and $\theta =\frac{1}{\nu }$ 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.