  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
quasiperiodic ground state to the high temperature disordered phase proceeds
through a sequence of periodic arrangements of rows, in analogy with the
Frenkel-Kontorova model, but with temperature playing the role of the strength
of the substrate potential.
