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Physical review. B, Condensed matter

Surface magnetism in a compressible Ising model

A. F. S. Moreira, W. Figueiredo

Published Aug 1, 1992• 5 citations
Publisher

Abstract

A semi-infinite compressible Ising model is studied within a variational approach based on Bogoliubov's inequality. The exchange couplings in our effective-spin Hamiltonian depend on external forces. We have determined the profile of the magnetization and the phase diagram for the surface critical couplings as a function of the external force.

DOI
10.1103/physrevb.46.2891

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A semi-infinite compressible Ising model is studied within a variational approach based on Bogoliubov's inequality. The exchange couplings in our effective-spin Hamiltonian depend on external forces. We have determined the profile of the magnetization and the phase diagram for the surface critical couplings as a function of the external force.
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We consider a semi-infinite two-dimensional Ising model with nearest-neighbor coupling constants that deviate from the bulk coupling by $A{m}^{\ensuremath{-}y}$ for large mmm, mmm being the distance from the edge. The case A<0A<0A<0 of couplings which are weaker near the surface has been discussed by Hilhorst and van Leeuwen. We report exact results for the boundary magnetization and boundary pair-correlation function when A>0A>0A>0. At the bulk critical temperature there is a rich variety of critical behavior in the $A \ensuremath{-}y$ plane with both paramagnetic and ferromagnetic surface phases. Some of our results can be derived and generalized with simple scaling arguments.