Entropic commensurate-incommensurate transition

The equilibrium properties of a minimal tiling model are investigated. The model has extensive ground state entropy, with each ground state having a quasiperiodic sequence of rows. It is found that the transition from the ground state to the high temperature disordered phase proceeds through a sequence of periodic arrangements of rows, in analogy with the commensurate-incommensurate transition. We show that the effective free energy of the model resembles the Frenkel-Kontorova Hamiltonian, but with temperature playing the role of the strength of the substrate potential, and with the competing lengths not explicitly present in the basic interactions.