Taras Yavors'kii

Ivan Franko Lviv State University

Yurij Holovatch

Institute for Condensed Matter Physics NAS of Ukraine

Reinhard Folk

Institute for Theoretical Physics, University of Linz
From renormalization group (RG) theory one knows that in the asymptotic region the values of the critical exponents are universal and scaling laws between them hold. There the couplings of the model Hamiltonian describing the critical system have reached their fixed point values. In the non-asymptotic region deviations from the fixed point values are present. They die out according to a universal power law governed by the correction to scaling exponent ω. The smaller the exponent, the larger is the region where corrections to the asymptotic power laws have to be taken into account.
The implication of quenched dilution on the critical behavior is a long-standing problem attracting theoretical, experimental and numerical efforts. In the 3D Ising model quenched disorder changes the asymptotic critical exponents compared to the pure ones [1,2]. In principle this statement should hold for arbitrary weak dilution. But in order to observe this change one should approach the critical point lose enough. The width of this region turns out to be dilution dependent.
[1] A.B. Harris. Effect of random defects on the critical behaviour of Ising models. J. Phys. C, 7 (1974) 1671.
[2] J.T. Chayes, et al. Finite-size scaling and correlation lengths for disordered systems. Phys. Rev. Lett. 57 (1986) 2999.
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