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

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

2001-07-06

arxiv.org/abs/cond-mat/0107139v1

Phys. Rev. Lett. 87, 176102 (2001)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 3 eps-figures included

Scientific paper

10.1103/PhysRevLett.87.176102

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 $\nu\approx1.3$, $\beta\approx0.05$, $\gamma/\nu\approx2.9$ 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$d$.

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