Disorder Driven Critical Behavior of Periodic Elastic Media in a Crystal Potential

Abstract

We study a lattice model of a three-dimensional periodic elastic medium at zero temperature with exact combinatorial optimization methods. A competition between pinning of the elastic medium, representing magnetic flux lines in the mixed phase of a superconductor or charge density waves in a crystal, by randomly distributed impurities and a periodic lattice potential gives rise to a continuous phase transition from a flat phase to a rough phase. We determine the critical exponents of this roughening transition via finite size scaling obtaining $\nu \approx 1.3$, $\beta \approx 0.05$, $\gamma /\nu \approx 2.9$ and find that they are universal with respect to the periodicity of the lattice potential. The small order parameter exponent is reminiscent of the random field Ising critical behavior in 3$d$.

4 pages, 3 eps-figures included

References in corpus (1)

• Intermittence and roughening of periodic elastic media

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