DOI: https://doi.org/10.30970/jps.03.422
CLASSICAL TO QUANTUM CROSSOVER OF THE CRITICAL BEHAVIOUR OF IMPURE SYSTEMS
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Journal of Physical Studies 3(4), 422–430 (1999)
DOI: https://doi.org/10.30970/jps.03.422 CLASSICAL TO QUANTUM CROSSOVER OF THE CRITICAL BEHAVIOUR OF IMPURE SYSTEMS |
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I. P. Takov
CPCM Laboratory, G. Nadjakov Institute of Solid State Physics,
Bulgarian Academy of Sciences
BG-1784 Sofia, Bulgaria
The classical–to–quantum dimensional crossover in a wide class of systems with quenched impurities and inhomogeneities is investigated within the framework of the renormalization group. The one–loop renormalization group equations are derived with the help of a double $(ϵ,δ)$–expansion, where the small parameter $δ$ describes the quantum effects and $ϵ=2σ-d$ is the usual expansion parameter $(0<σ\leq 2;\ d $ is the spatial dimensionality). The classical–to–quantum crossover phenomenon is established and the critical exponents are calculated to first order in $ϵ$ and $δ$. The analogy between this approach and that of double $(ϵ, δ)$–expansion in treating the extended impurities problem is discussed.