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 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.

20 pages, 6 figures, uses elsart.sty, to be published in Physica A

References in corpus (6)

• Ordinary, extraordinary, and normal surface transitions: extraordinary-normal equivalence and simple explanation of $|T-T_c{|}^{2-\alpha }$ singularities
• Multibondic Cluster Algorithm for Monte Carlo Simulations of First-Order Phase Transitions
• Monte Carlo Simulation of Universal Short-Time Behavior in Critical Relaxation
• Near-Surface Long-Range Order at the Ordinary Transition
• Long-time traces of the initial condition in relaxation phenomena near criticality
• Dynamical Relaxation and Universal Short-Time Behavior in Finite Systems: The Renormalization Group Approach

Cited by in corpus (9)

• Generalized Dynamic Scaling for Critical Magnetic Systems
• Critical Casimir effect in classical binary liquid mixtures
• Critical phenomena at perfect and non-perfect surfaces
• Water in nanopores. II. Liquid-vapour phase transition near hydrophobic surfaces
• Critical Casimir forces for Ising films with variable boundary fields
• Effects of weak surface fields on the density profiles and adsorption of a confined fluid near bulk criticality
• Critical adsorption and critical Casimir forces in the canonical ensemble
• X-Ray Scattering at FeCo(001) Surfaces and the Crossover between Ordinary and Normal Transitions
• Nonequilibrium critical dynamics of the two-dimensional Ising model quenched from a correlated initial state