Conformal Invariance in (2+1)-Dimensional Stochastic Systems

Details Conformal Invariance in (2+1)-Dimensional Stochastic Systems Conformal Invariance in (2+1)-Dimensional Stochastic Systems

2009-09-14

arxiv.org/abs/0909.2661v2

Physics

Condensed Matter

Statistical Mechanics

Title, abstract and part of the text have been rewritten. To be published in Physical Review E.

Scientific paper

Stochastic partial differential equations can be used to model second order thermodynamical phase transitions, as well as a number of critical out-of-equilibrium phenomena. In (2+1) dimensions, many of these systems are conjectured (and some are indeed proved) to be described by conformal field theories. We advance, in the framework of the Martin-Siggia-Rose field theoretical formalism of stochastic dynamics, a general solution of the translation Ward identities, which yields a putative conformal energy-momentum tensor. Even though the computation of energy-momentum correlators is obstructed, in principle, by dimensional reduction issues, these are bypassed by the addition of replicated fields to the original (2+1)-dimensional model. The method is illustrated with an application to the Kardar-Parisi-Zhang (KPZ) model of surface growth. The consistency of the approach is checked by means of a straightforward perturbative analysis of the KPZ ultraviolet region, leading, as expected, to its $c=1$ conformal fixed point.

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