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Journal of Physics C Solid State Physics

Diluted quantum transverse Ising model

Robin B. Stinchcombe

Published Apr 10, 1981• 50 citations
Publisher

Abstract

An extract scaling of the diluted zero temperature transverse Ising chain is used to obtain its exact quantum critical behaviour. The extension, by an approximate cluster method, of the approach to the diluted two-dimensional zero temperature transverse Ising model yields a discontinuity at the percolation concentration in the dependence of critical field on concentration, as conjectured by Harris (1974).

DOI
10.1088/0022-3719/14/10/003

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An extract scaling of the diluted zero temperature transverse Ising chain is used to obtain its exact quantum critical behaviour. The extension, by an approximate cluster method, of the approach to the diluted two-dimensional zero temperature transverse Ising model yields a discontinuity at the percolation concentration in the dependence of critical field on concentration, as conjectured by Harris (1974).
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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.