Conformal Invariance in 2 1-Dimensional Stochastic Systems - Condensed Matter > Statistical MechanicsReport as inadecuate




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Abstract: Stochastic partial differential equations can be used to model second orderthermodynamical phase transitions, as well as a number of criticalout-of-equilibrium phenomena. In 2+1 dimensions, many of these systems areconjectured and some are indeed proved to be described by conformal fieldtheories. We advance, in the framework of the Martin-Siggia-Rose fieldtheoretical formalism of stochastic dynamics, a general solution of thetranslation Ward identities, which yields a putative conformal energy-momentumtensor. Even though the computation of energy-momentum correlators isobstructed, in principle, by dimensional reduction issues, these are bypassedby the addition of replicated fields to the original 2+1-dimensional model.The method is illustrated with an application to the Kardar-Parisi-Zhang KPZmodel of surface growth. The consistency of the approach is checked by means ofa straightforward perturbative analysis of the KPZ ultraviolet region, leading,as expected, to its $c=1$ conformal fixed point.



Author: L. Moriconi, M. Moriconi

Source: https://arxiv.org/







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