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

Peter Czerner and Uwe Ritschel

Physica A: Statistical Mechanics and its Applications, 1997, vol. 237, issue 1, 240-256

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 H1 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) ≈ H1z1−η∼ord, predicted for a smallH1 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.

Keywords: Surface critical phenomena; Critical adsorption; Ising model; Monte Carlo simulation (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:237:y:1997:i:1:p:240-256

DOI: 10.1016/S0378-4371(96)00411-6

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