Disorder-driven critical behavior of periodic elastic media in a crystal potential.

A lattice model of a three-dimensional periodic elastic medium at zero temperature is studied with exact combinatorial optimization methods. A competition between pinning of the elastic medium, representing magnetic flux lines in a superconductor or charge density waves in a crystal, by randomly distributed impurities and a periodic lattice potential gives rise to a continuous roughening transition from a flat to a rough phase. A finite size scaling analysis yields the critical exponents nu approximately 1.3, beta approximately 0.05, gamma/nu approximately 2.9 that 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 3D.