Surface and bulk transitions in three-dimensional O(n) models.

Abstract

Using Monte Carlo methods and finite-size scaling, we investigate surface criticality in the O(n) models on the simple-cubic lattice with n=1 , 2, and 3, i.e., the Ising, XY , and Heisenberg models. For the critical couplings we find Kc (n=2) =0.454 1659 (10) and Kc (n=3) =0.693 003 (2). We simulate the three models with open surfaces and determine the surface magnetic exponents at the ordinary transition to be y (o)(h1) =0.7374 (15) , 0.781 (2), and 0.813 (2) for n=1 , 2, and 3, respectively. Then we vary the surface coupling K1 and locate the so-called special transition at kappa(c) (n=1) =0.502 14 (8) and kappa(c) (n=2) =0.6222 (3), where kappa= K1 /K-1 . The corresponding surface thermal and magnetic exponents are y (s)(t1) =0.715 (1) and y (s)(h1) =1.636 (1) for the Ising model, and y(s)(t1) =0.608 (4) and y(s)(h1) =1.675 (1) for the XY model. Finite-size corrections with an exponent close to -1/2 occur for both models. Also for the Heisenberg model we find substantial evidence for the existence of a special surface transition.