Near-Surface Long-Range Order at the Ordinary Transition: Scaling Analysis and Monte Carlo Results

TL;DR

This paper investigates the near-surface order parameter behavior in 3D Ising models near the ordinary transition, combining scaling theory and Monte Carlo simulations to understand surface critical phenomena.

Contribution

It provides a detailed scaling analysis and Monte Carlo validation of the near-surface magnetization behavior at the ordinary transition with surface fields.

Findings

Power-law increase of surface magnetization confirmed by simulations

Scaling arguments successfully describe crossover behavior

Relevance to experimental critical adsorption phenomena

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 power-law increase of the magnetization, 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.