Two-Dimensional Models of Commensurate-Incommensurate Phase Transitions

Marcelo D. Grynberg

Steven F. Howes, Leo P. Kadanoff, Marcel den Nijs

William R. Schief

Béla Joós, B. Bergersen, Robert J Gooding +1 more

We present a renormalization argument for the discrete linear chain with a harmonic interparticle interaction and a sinusoidal substrate potential. We find that there exists a critical value of the substrate potential above which the incommensurate phase lying in between two successive registered phases is a complete devil's staircase of commensurate states. For weaker substrate potentials, the devil's staircase is partially incomplete. Near the commensurate-incommensurate transition it consists only of commensurate states, while at higher soliton densities the commensurate states are separated by truly incommensurate states. These results are in agreement with the findings of previous authors using different methods.

Michael N. Barber

Wenfei Li, Hyunggyu Park

The authors study finite-size-scaling behaviour of a two-dimensional random tiling model. This model exhibits commensurate-incommensurate phase transitions of the Pokrovsky-Talapov type where anisotropic scaling appears. A simple scaling argument near this transition suggests an integral surface critical exponent which, in turn, implies a logarithmic singularity with a universal coefficient in the surface free energy. They confirm the existence of this singularity numerically employing the transfer matrix method in the case of free boundary conditions.