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Journal of Physics A Mathematical and General

Quenched impurities and tricriticality in classical and quantum systems

Gaetano Busiello, L. De Cesare, Dimo I. Uzunov

Published Jun 1, 1984• 6 citations
Publisher

Abstract

A generalised model, intended to describe a number of quantum systems in the presence of short-range correlated quenched impurities, is studied by the renormalisation group approach. To first order in epsilon , it is shown that the tricritical behaviour is unstable towards impurity perturbations for both finite and zero temperatures. A brief discussion of the zero-temperature tricriticality in pure systems is also presented.

DOI
10.1088/0305-4470/17/8/010

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The authors use a Migdal-Kadanoff renormalisation group to study the behaviour of the Blume-Emery-Griffiths model when quenched, random-bond dilution is introduced. Phase diagrams are calculated for varying dilution. The behaviour of the multicritical points of the pure system as dilution is introduced is of particular interest. They find that the tricritical temperature tends to zero as the percolation threshold is approached but that the tricritical field remains finite in agreement with experimental results on the dilute metamagnet Fe p Mg (1-p) Cl 2 .
The effects of short-range-correlated impurities on the critical behavior of some quantum models with a free-energy spectrum $\ensuremath{\sim}{k}^{\ensuremath{\sigma}}(0<\ensuremath{\sigma}<~2)$ are investigated by using the renormalization-group approach via the replica trick. At zero temperature, two nonsimultaneous expansion parameters ${\ensuremath{\epsilon}}_{q}={d}_{q}\ensuremath{-}d({d}_{q}=\ensuremath{\sigma}$ or $\frac{3}{2}\ensuremath{\sigma}$) and $\ensuremath{\epsilon}=2\ensuremath{\sigma}\ensuremath{-}d$ are involved in terms of which an unusual phase transition is predicted for $d<2\ensuremath{\sigma}$.
The theoretic renormalization-group approach is applied to the study of short-time critical behavior of the ddd-dimensional spin systems (model A) in the presence of quenched impurities with a long-range correlations decaying as ${r}^{\ensuremath{-}(d\ensuremath{-}\ensuremath{\rho})}$. The asymptotic scaling laws are studied in the frame of a double expansion in $ϵ=4\ensuremath{-}d$ and $\ensuremath{\rho}$ with $\ensuremath{\rho}$ of order ϵϵϵ. In d<4d<4d<4, the initial slip exponents ${\ensuremath{\theta}}^{\ensuremath{'}}$ of the magnetization and $\ensuremath{\theta}$ of the response function, are calculated up to two-loop order. The crossover between fixed points is obtained. The long-time limit of the fluctuation-dissipation ratio is found in the aging regime, and its connection to equilibrium quantities is discussed. The comparison of our results with those of other systems without long-range correlated quenched impurities is also investigated.