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 $2D$, 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.