Abstract
We demonstrate a three-dimensional Kosterlitz-Thouless (KT) transition in the random field model driven out of thermal equilibrium. By employing the spin-wave approximation and functional renormalization group approach, in the weak disorder regime, the three-dimensional driven random field model is found to exhibit a quasi-long-range order phase, wherein the correlation function shows power-law decay with a nonuniversal exponent that depends on the disorder strength. This result is consistent with that reported in a previous numerical study. We further develop a phenomenological theory of the three-dimensional KT transition by taking into account the effect of vortices. The point of this theory is that the cross-section of the system with respect to a plane perpendicular to the driving direction is essentially identical to the two-dimensional pure model.
- Received 31 March 2017
- Revised 10 August 2018
DOI:https://doi.org/10.1103/PhysRevE.98.032122
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