Date of Original Version
Universality of surface critical behavior with respect to surface enhancement is studied for O(n) models with n=1 (Ising), n=2 (planar rotor), and n=3 (Heisenberg) on simple-cubic lattices. Finite-size methods are employed to estimate surface critical exponents for ordinary surface criticality. In addition, it is shown that universal scaling functions, independent of surface enhancement, can be constructed with all nonuniversal features of the finite-size scaling function of the spin-spin surface correlation functions incorporated in (1) a metric factor and (2) an irrelevant scaling field associated with the surface coupling strength.
Nightingale, M. P., & Blöte, H. W. J. (1993). Universality of surface correlation functions in three-dimensional models. Physical Review B, 48(18), 13678-13683. doi: 10.1103/PhysRevB.48.13678
Available at: http://dx.doi.org/10.1103/PhysRevB.48.13678