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Journal of Physics C Solid State Physics

The dilute Ising antiferromagnet in a uniform field on a square lattice

S. L. A. de Queiroz, Raimundo R. dos Santos

Published Apr 10, 1988• 6 citations
Publisher

Abstract

The bond-diluted Ising antiferromagnet in a uniform field (DAFF) on a square lattice is studied and comparison with the random-field problem is made. Position-space renormalisation group calculations for the DAFF give rise to a staircase structure in the zero-temperature phase boundary H (critical field) versus p (bond concentration), separating ordered and disordered phases. Since there is no stable long-range order in the equivalent random-field system, the authors discuss ways in which a consistent picture can be obtained, incorporating both our results and the correspondence between the two problems.

DOI
10.1088/0022-3719/21/10/017

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The bond-diluted Ising antiferromagnet in a uniform field (DAFF) on a square lattice is studied and comparison with the random-field problem is made. Position-space renormalisation group calculations for the DAFF give rise to a staircase structure in the zero-temperature phase boundary H (critical field) versus p (bond concentration), separating ordered and disordered phases. Since there is no stable long-range order in the equivalent random-field system, the authors discuss ways in which a consistent picture can be obtained, incorporating both our results and the correspondence between the two problems.
A zero-temperature real space renormalisation group block method is applied to the random quantum Ising model with a transverse field on the planar honeycomb and square lattices. For the bound diluted system the magnetisation and the separation of the ground-state energy level (in the paramagnetic phase) are presented for several bond concentrations p. The critical exponents extracted both from the fixed points and from direct numerical computations preserve some scaling relations, and the critical curve displays a characteristic discontinuity at the percolation concentration. For the McCoy and Wu distribution (1968) the random fields and bonds are found to introduce a strong relevant disorder. The order parameter still falls off continuously to zero for well defined values of the parameters but a new fixed point yields a slight change in the critical exponents.
2D spin-1 Ising models with nearest-neighbour and crystal-field interactions exhibit tricritical behaviour. A new method that applies to a wide class of random systems is used to study the influence of site and bond dilution on this behaviour. The authors have calculated temperature-crystal-field-concentration phase diagrams and determined, in particular, the influence of dilution on the zero-temperature critical field and on the tricritical temperature. The results are in agreement with those obtained recently for bond dilution by a real-space renormalisation-group technique. The method appears more tractable.
The antiferromagnetic Ising model in a uniform field on a square lattice is studied by a position-space renormalisation group approach. A self-dual cluster that preserves sublattice symmetry is employed: at each site of the cluster, the coupling to the field is chosen to be proportional to the coordination number of that site. The author obtains the physically correct result that the magnetic field is irrelevant (in the renormalisation group sense) near the zero-field fixed point. The phase diagram he obtains compares well with experimental results for CoCs 3 Br 5 and with the conjectured analytic form postulated by Muller-Hartmann and Zittartz. He discusses possible applications of this approach to other situations of interest.