Surface and Bulk Transitions in Three-Dimensional O(n) Models

Authors

Youjin Deng
Henk W.J. Blöte
M. P. Nightingale, University of Rhode IslandFollow

Document Type

Article

Date of Original Version

7-27-2005

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 K_c(n=2)=0.4541659 (10) and K_c(n=3)=0.693003 (2). We simulate the three models with open surfaces and determine the surface magnetic exponents at the ordinary transition to be y_h1^(o)=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 κ_c(n=1)=0.50214 (8) and κ_c(n=2)=0.6222 (3), where κ=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.

Citation/Publisher Attribution

Deng, Y., Blöte, H. W.J., & Nightingale, M. P. (2005). Surface and bulk transitions in three-dimensional O(n) models. Physical Review E, 72(1), 016128. doi: 10.1103/PhysRevE.72.016128

Available at: http://dx.doi.org/10.1103/PhysRevE.72.016128

Publisher Statement

©2005 The American Physical Society