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physica status solidi (b)

Critical Properties of Bond‐ and Site‐Diluted Triangular Lattice Ising Model

L. R. Evangelista, V. K. Saxena

Published Sep 1, 1986• 1 citation
Publisher
DOI
10.1002/pssb.2221370142

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The hypothesis of weak universality is tested for the moments of the zero-field correlation function and the magnetic-field derivatives of the free energy of dilute Ising models. The investigation, which is carried out for dilution of both the magnetic sites (site dilution) and interactions (bond dilution), is performed just above the critical temperature. In the case of bond dilution both the quenched and annealed distributions are considered. The quenched model is investigated by series methods for site and bond dilution on the face-centred cubic lattice and for bond dilution on the triangular lattice.
A position space renormalisation group technique (decimation) is used to treat site- and bond-diluted Ising ferromagnets on square and triangular lattices. In every case the renormalisation equations lead to two fixed points, one corresponding to the pure Ising system and one to percolation. Linearising around the fixed points, eigenvalues and hence the critical exponents nu T , nu P (correlation length), alpha (specific heat) and phi (crossover) are obtained. Numerical iteration of the recursion relations provides the critical curves. Values of critical temperatures, critical concentrations, exponents, and of limiting slopes of critical curves are in very satisfactory agreement with all known exact or series results. Points on the critical curve flow into the Ising fixed point under the transformation. The sign of the pure Ising exponent alpha is consistent with this flow for the site-diluted cases but not for the bond-diluted cases.