We have studied the critical behavior of a generalized Frenkel-Kontorova model in which the external potential is nonanalytic and has a variable degree of inflection z. For z>3 a sequence of pinning and depinning transitions has been observed. The critical exponents of the gap in the phonon spectrum, the coherence length, and the Peierls-Nabarro barrier of the ground state are found to vary with z when 2≤z<3, but are independent of z when z≥3. It suggests that the degree of inflection plays a role quite similar to that of dimensionality, with z=2 and 3 corresponding, respectively, to the lower and upper critical dimensions.

• Received 14 November 1991

DOI:https://doi.org/10.1103/PhysRevA.45.5455