Near-surface long-range order at the ordinary transition: scaling analysis and Monte Carlo results
✍ Scribed by Peter Czerner; Uwe Ritschel
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 924 KB
- Volume
- 237
- Category
- Article
- ISSN
- 0378-4371
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✦ Synopsis
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 re(z) obtained with the Swendsen-Wang algorithm. In particular the sharp power-law increase of the magnetization, m(z) ~ HI z 1-~d, predicted for a small HI 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.