Nonequilibrium Kosterlitz-Thouless Transition in the Three-Dimensional Driven Random Field XY Model

  • Taiki HagaEmail author
Part of the Springer Theses book series (Springer Theses)


We consider the driven random field XY model. The dimensional reduction predicts that this model exhibits the Kosterlitz-Thouless transition in three dimensions. We investigate this remarkable conjecture by using numerical simulations and renormalization group analysis. In the first part of this chapter, we show several results of the numerical simulations of the driven random field XY model. These results suggest that there is a transition between a quasi-long-range order phase at weak disorder and a disordered phase at strong disorder. The second half of this chapter is devoted to the functional renormalization group analysis of this model. Within the spin-wave approximation, the driven random field XY model is shown to exhibit a quasi-long-range order with a nonuniversal exponent at weak disorder. We also construct a phenomenological theory of the three-dimensional Kosterlitz-Thouless transition by taking into account the effect of topological defects.


Driven disordered systems Dynamical reordering transition Dimensional reduction Functional renormalization group 


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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of PhysicsKyoto UniversityKyotoJapan

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