Dimensional reduction and its breakdown in the driven random field O(N) model

Abstract

The critical behavior of the random field $O(N)$ model driven at a uniform velocity is investigated at zero-temperature. From naive phenomenological arguments, we introduce a dimensional reduction property, which relates the large-scale behavior of the $D$-dimensional driven random field $O(N)$ model to that of the $(D-1)$-dimensional pure $O(N)$ model. This is an analogue of the dimensional reduction property in equilibrium cases, which states that the large-scale behavior of $D$-dimensional random field models is identical to that of $(D-2)$-dimensional pure models. However, the dimensional reduction property breaks down in low enough dimensions due to the presence of multiple meta-stable states. By employing the non-perturbative renormalization group approach, we calculate the critical exponents of the driven random field $O(N)$ model near three-dimensions and determine the range of $N$ in which the dimensional reduction breaks down.

20 pages, 7 figures

References in corpus (6)

• Non-perturbative fixed point in a non-equilibrium phase transition
• Nematic-Isotropic Transition with Quenched Disorder
• Phase transitions in disordered systems: the example of the random-field Ising model in four dimensions
• Restoration of dimensional reduction in the random-field Ising model at five dimensions
• Infrared behavior and spectral function of a Bose superfluid at zero temperature
• Two-loop Functional Renormalization Group of the Random Field and Random Anisotropy O(N) Models

Cited by in corpus (4)

• Random-field Ising and $O(N)$ models: Theoretical description through the functional renormalization group
• Nonequilibrium Kosterlitz-Thouless transition in a three-dimensional driven disordered system
• Dimensional reduction in driven disordered systems
• Machine learning analysis of dimensional reduction conjecture for nonequilibrium Berezinskii-Kosterlitz-Thouless transition in three dimensions