Near-surface long-range order at the ordinary transition: scaling analysis and Monte Carlo results

Abstract

Motivated by recent experimental activities on surface critical phenomena, we present a detailed theoretical study of the near-surface behavior of the local order parameter m( z) in Ising-like spin systems. Special attention is paid to the crossover regime between “ordinary” and “normal” transition in the three-dimensional semi-infinite Ising model, where a finite magnetic field H 1 is imposed on the surface which itself exhibits a reduced tendency to order spontaneously. As the theoretical foundation, the spatial behavior of m( z) is discussed by means of phenomenological scaling arguments, and a finite-size scaling analysis is performed. Then we present Monte Carlo results for m( z) obtained with the Swendsen-Wang algorithm. In particular the sharp power-law increase of the magnetization, m( z) ≈ H 1 z 1− η ∼ ord , predicted for a small H 1 by previous work of the authors, is corroborated by the numerical results. The relevance of these findings for experiments on critical adsorption in systems where a small effective surface field occurs is pointed out.