Critical behaviour near multiple junctions and dirty surfaces in the two-dimensional Ising model

Details Critical behaviour near multiple junctions and dirty surfaces in the two-dimensional Ising model Critical behaviour near multiple junctions and dirty surfaces in the two-dimensional Ising model

2001-06-29

arxiv.org/abs/cond-mat/0106626v1

J. Phys. A 24 (1991) 1031

Physics

Condensed Matter

Statistical Mechanics

Old paper, for archiving. 6 pages, 1 figure, IOP macro, epsf

Scientific paper

10.1088/0305-4470/24/17/012

We consider m two-dimensional semi-infinite planes of Ising spins joined together through surface spins and study the critical behaviour near to the junction. The m=0 limit of the model - according to the replica trick - corresponds to the semi-infinite Ising model in the presence of a random surface field (RSFI). Using conformal mapping, second-order perturbation expansion around the weakly- and strongly-coupled planes limits and differential renormalization group, we show that the surface critical behaviour of the RSFI model is described by Ising critical exponents with logarithmic corrections to scaling, while at multiple junctions (m>2) the transition is first order. There is a spontaneous junction magnetization at the bulk critical point.

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