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Le Journal de Physique Colloques

SURFACE MAGNETIC ORDER AND EFFECTS OF THE NATURE OF THE INTERACTIONS

Constantino Tsallis, Anna Chame

Published Dec 1, 1988• 9 citations
Publisher

Abstract

We discuss, within a real-space renormalization-group, interesting thermal effects (surface singularity at the bulk transition ; Ising-Heisenberg crossover) concerning the free surface of a semi-infinite d = 3 spin 1/2 anisotropic Heisenberg ferromagnet. Comparison with the Mermin-Wagner theorem and with experimental work is done.
DOI
10.1051/jphyscol:19888741

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We use simple position-space renormalization-group procedures involving only nearest-neighbor interactions to discuss the critical behavior of the ferromagnetically coupled semi-infinite Ising model with a free surface in two and three dimensions. In three dimensions for suitably enhanced surface couplings there are surface transitions and simultaneous surface-bulk transitions as well as the bulk transition. A phase diagram, critical exponents for the various transitions, and some representative magnetization profiles are calculated. Despite their simplicity, the renormalization transformations exhibit complete sets of fixed points for describing the various phase transitions and yield phase diagrams which are a significant improvement over mean-field theory. However, the calculated magnetization profiles show some unphysical features due to the finite cluster size on which the transformations are based.