Finite-size effects in layered magnetic systems

Thermal and magnetic effects in a system consisting of thin layers of coupled Ising spins with S=1/2 and S=1 are considered. The specific heat and the correlation length display maxima at two different temperatures. It is discussed in what sense these maxima can be interpreted as a finite-size rounding of a thermodynamic singularity associated with a phase transition. The connection with ordinary, extraordinary, and special surface phase transitions is made. In two dimensions (2D), the surface critical exponents are calculated from conformal invariance. The bulk and surface finite-size scaling of the order-parameter profiles at the transition points is discussed. In 2D, an exact scaling function for the profiles is suggested through conformal invariance arguments for the (extra)ordinary transition.