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Physics Letters A

On the critical behaviour of disordered systems

Uwe Krey

Published Mar 1, 1975• 33 citations
Publisher
DOI
10.1016/0375-9601(75)90524-1

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The author has investigated the critical behaviour of site-disordered Ising systems over a large range of dilution (0.6<or=p<or=1.0) investing about 10 15 single spin flips with conventional local dynamics. Critical temperatures have been determined with high-precision using the cumulant method. The finite-size simulations lead to concentration-dependent exponents which seem to violate universality. The author shows that the concentration dependence is induced by a crossover phenomenon which governs a large interval of the critical region. The author finds that the scaling functions of systems with different disorder converge asymptotically to universal behaviour consistent with the fixed point of weak disorder.

Journal of Physics A Mathematical and General•Mar 21, 1993•70 citations
A eld-theoretic description of the critical behaviour of the weakly disordered systems is given.Directly, for three-and two-dimensional systems a renormalization analysis of the eective Hamiltonian of the model with replica symmetry breaking (RSB) potentials is carried out in the two-loop approximation.For the case with rst-step RSB the xed points (FPs) corresponding to the stability of the various types of critical behaviour are identi ed with the use of the Pad e{Borel summation technique.The analysis of FPs has shown a stability of the critical behaviour of the weakly disordered three-and two-dimensional systems with respect to RSB eects and realization of the former scenario of disorder in uence on critical behaviour.For the case of systems with arbitrary dimension from 3 to 4 the ranges of critical behaviour determined by the RSB eects are found for each value of the p-component order parameter without the use of "-expansion.A comparison with the results of the "-expansion calculations is carried out.
The author has investigated the critical behaviour of site-disordered Ising systems over a large range of dilution (0.6<or=p<or=1.0) investing about 10 15 single spin flips with conventional local dynamics. Critical temperatures have been determined with high-precision using the cumulant method. The finite-size simulations lead to concentration-dependent exponents which seem to violate universality. The author shows that the concentration dependence is induced by a crossover phenomenon which governs a large interval of the critical region. The author finds that the scaling functions of systems with different disorder converge asymptotically to universal behaviour consistent with the fixed point of weak disorder.