Abstract
We study the problem of the condensate (stochastic average) origination for an auxiliary field in the Kardar-Parisi-Zhang equation and its matrix generalization. We cannot reliably conclude that there is a condensate for the Kardar-Parisi-Zhang equation in the framework of the one-loop approximation improved by the renormalization group method. The matrix generalization of the Kardar-Parisi-Zhang equation permits a positive answer to the question of whether there is a nonzero condensate, and the problem can be solved exactly in the large-N limit.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 178, No. 3, pp. 416–432, March, 2014.
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Bork, L.V., Ogarkov, S.L. The Kardar-Parisi-Zhang equation and its matrix generalization. Theor Math Phys 178, 359–373 (2014). https://doi.org/10.1007/s11232-014-0148-z
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DOI: https://doi.org/10.1007/s11232-014-0148-z