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Dimensional Reduction and its Breakdown in the Driven Random Field O(N) Model

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

Abstract

We investigate the critical behavior of the driven random field O(N) model. First, from an intuitive argument, we derive a new dimensional reduction property, which predicts that the critical behavior of the driven disordered system at zero temperature is the same as that of the lower dimensional pure system in equilibrium. However, this dimensional reduction breaks down in low enough dimensions due to a nonperturbative effect associated with meta-stable states. By employing the nonperturbative formalism of the functional renormalization group, we derive the flow equation of the renormalized disorder correlator and clarify the condition that the dimensional reduction fails. We also calculate the critical exponents near three dimensions.We investigate the critical behavior of the driven random field O(N) model. First, from an intuitive argument, we derive a new dimensional reduction property, which predicts that the critical behavior of the driven disordered system at zero temperature is the same as that of the lower dimensional pure system in equilibrium. However, this dimensional reduction breaks down in low enough dimensions due to a nonperturbative effect associated with meta-stable states. By employing the nonperturbative formalism of the functional renormalization group, we derive the flow equation of the renormalized disorder correlator and clarify the condition that the dimensional reduction fails. We also calculate the critical exponents near three dimensions.

Keywords

Driven disordered systems Dynamical reordering transition Dimensional reduction Functional renormalization group 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of PhysicsKyoto UniversityKyotoJapan

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