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Physical review. B, Condensed matter

Mean-field renormalization-group approaches to the surface on a semi-infinite Ising model with a random surface field

Gang Sun

Published Feb 1, 1995• 1 citation
Publisher

Abstract

We study the critical behavior of the surface on a semi-infinite simple-cubic-lattice Ising model with a bimodal random surface field by a large-cell mean-field renormalization-group method. Our results show that a surface ferromagnetic phase exists at weak random fields above the bulk critical temperature, and no signs of the tricritical point are found until the surface critical temperature decreases to that of the bulk.

DOI
10.1103/physrevb.51.3637

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We study the critical behavior of the surface on a semi-infinite simple-cubic-lattice Ising model with a bimodal random surface field by a large-cell mean-field renormalization-group method. Our results show that a surface ferromagnetic phase exists at weak random fields above the bulk critical temperature, and no signs of the tricritical point are found until the surface critical temperature decreases to that of the bulk.
We study the critical behavior of the surface on a semi-infinite simple cubic lattice Ising model with a bimodal random surface field by large cell mean-field renormalization group method and Monte Carlo simulations. Our results show that the surface ferromagnetic phase exists in the weak random field range above the bulk critical temperature. The surface specific heat is not divergence and the susceptibility show a cusp singularity at the surface ferromagnetic-paramagnetic transition for a relatively large random field.
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.
A semi-infinite Ising model on a simple-cubic lattice, bounded by two perpendicular planes which meet at an edge, is studied with the Migdal-Kadanoff renormalization-group approach. It is found that the edge spins can order at a temperature higher than the bulk transition temperature if one of the surfaces is also ordered, whereas no edge ordering is possible if none of the surfaces nor the bulk are ordered. A complete phase diagram is presented in the parameter space of the model considered. Correlation-length critical exponents \ensuremath{\nu} and the crossover exponent \ensuremath{\varphi} are calculated and various universality classes are established.