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arXiv:cond-mat/9805189 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Surface critical behavior of driven diffusive systems with open boundaries

Klaus Oerding, H. K. Janssen

Published Aug 1, 1998• 10 citations
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Abstract

Using field theoretic renormalization group methods we study the critical behavior of a driven diffusive system near a boundary perpendicular to the driving force. The boundary acts as a particle reservoir, which is necessary to maintain the critical particle density in the bulk. The scaling behavior of correlation and response functions is governed by a new exponent ${\ensuremath{\eta}}_{1},$ which is related to the anomalous scaling dimension of the chemical potential of the boundary. The new exponent and a universal amplitude ratio for the density profile are calculated at first order in $\ensuremath{\epsilon}=5\ensuremath{-}d.$ Some of our results are checked by computer simulations.

DOI
10.1103/physreve.58.1446

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Using field theoretic renormalization group methods we study the critical behavior of a driven diffusive system near a boundary perpendicular to the driving force. The boundary acts as a particle reservoir, which is necessary to maintain the critical particle density in the bulk. The scaling behavior of correlation and response functions is governed by a new exponent \ensuremathη1,{\ensuremath{\eta}}_{1},\ensuremathη1​, which is related to the anomalous scaling dimension of the chemical potential of the boundary. The new exponent and a universal amplitude ratio for the density profile are calculated at first order in \ensuremathϵ=5\ensuremath−d.\ensuremath{\epsilon}=5\ensuremath{-}d.\ensuremathϵ=5\ensuremath−d. Some of our results are checked by computer simulations.
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An introduction into the theory of boundary critical phenomena and the application of the field-theoretical renormalization group method to these is given. The emphasis is on a discussion of surface critical behavior at bulk critical points of magnets, binary alloys, and fluids. Yet a multitude of related phenomena are mentioned. The most important distinct surface universality classes that may occur for a given universality class of bulk critical behavior are described, and the respective boundary conditions of the associated field theories are discussed. The short-distance singularities of the order-parameter profile in the diverse asymptotic regimes are surveyed.
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We study the local critical behavior near the free surface of a d-dimensional system with a smooth inhomogeneity induced by a defect of dimension d∗{\mathit{d}}^{\mathrm{*}}d∗\ensuremath{\le}d-1 located on the surface. The couplings deviate from their bulk critical value by \ensuremath{\lambda}${\mathit{r}}_{\mathrm{\ensuremath{\perp}}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}}}$ where ${\mathit{r}}_{\mathrm{\ensuremath{\perp}}}$ is the distance to the center of the defect. Using a phenomenological approach, the change in the surface critical exponents is calculated to first order in the perturbation amplitude \ensuremath{\lambda} when the system is marginal, i.e., when the decay exponent of the perturbation \ensuremath{\alpha} is equal to the scaling dimension ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{\ensuremath{\varepsilon}}}^{0}$ of the bulk energy-density operator. Finally, the critical behavior near extended defects in the bulk is compared to the surface case.