Surface phases and surface phase transitions: A renormalization-group approach

The statistical mechanical description of a magnetic sample with a simple flat free surface is reviewed. Within the context of the ferromagnetic Ising model, expected surface thermodynamic behavior, with particular emphasis on surface phases, surface phase transitions, and related strong-coupling phenomena are outlined. Finally, a description is given of how strong-coupling and global thermodynamic properties of surfaces may be calculated using renormalization-group techniques. Calculated surface-energy curves for several two-and three-dimensional systems are given as examples. The two-dimensional calculations are in good agreement with exact results. The three-dimensional calculations, though cruder, display an intriguing variety of different types of behavior.