Abstract
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.
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Haga T (2015) Nonequilibrium quasi-long-range order of a driven random-field \(O(N)\) model. Phys Rev E 92:062113
Haga T (2018) Nonequilibrium Kosterlitz-Thouless transition in a three-dimensional driven disordered system. Phys Rev E 98:032122
Giamarchi T, Le Doussal P (1996) Moving glass phase of driven lattices. Phys Rev Lett 76:3408
Le Doussal P, Giamarchi T (1998) Moving glass theory of driven lattices with disorder. Phys Rev B 57:11356
Balents L, Marchetti MC, Radzihovsky L (1998) Nonequilibrium steady states of driven periodic media. Phys Rev B 57:7705
Goldenfeld N (1992) Lectures on phase transitions and the renormalization group. Westview Press
Garanin DA, Chudnovsky EM, Proctor T (2013) Random field XY model in three dimensions. Phys Rev B 88:224418
Ozeki Y, Ito N (2007) Nonequilibrium relaxation method. J Phys A Math Gen 40:R149
Ozeki Y, Ogawa K, Ito N (2003) Nonequilibrium relaxation analysis of Kosterlitz-Thouless phase transition. Phys Rev E 67:026702
Le Doussal P, Wiese KJ, Chauve P (2004) Functional renormalization group and the field theory of disordered elastic systems. Phys Rev E 69:026112
Le Doussal P, Wiese KJ (2006) Random-field spin models beyond 1 loop. Phys Rev Lett 96:197202
Jose JV, Kadanoff LP, Kirkpatrick S, Nelson DR (1977) Renormalization, vortices, and symmetry-breaking perturbation in the two-dimensional planar model. Phys Rev B 16:1217
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Haga, T. (2019). Nonequilibrium Kosterlitz-Thouless Transition in the Three-Dimensional Driven Random Field XY Model. In: Renormalization Group Analysis of Nonequilibrium Phase Transitions in Driven Disordered Systems. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-13-6171-5_5
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DOI: https://doi.org/10.1007/978-981-13-6171-5_5
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