Abstract
We present a simplified polymer model for twist-boundary phases in liquid crystals. The thermodynamic phases of this model are characterized by an angle 2\ensuremath{\pi}\ensuremath{\alpha}\ifmmode \tilde{}\else \~{}\fi{}. There are incommensurate phases with \ensuremath{\alpha}\ifmmode \tilde{}\else \~{}\fi{} an irrational number and commensurate phases with \ensuremath{\alpha}\ifmmode \tilde{}\else \~{}\fi{}=P/Q, with P and Q relatively prime integers. The latter have quasicrystalline symmetry for Q=5 or Q>6. Equilibrium phases with all values of \ensuremath{\alpha}\ifmmode \tilde{}\else \~{}\fi{} can be produced by varying a control parameter \ensuremath{\alpha}. The curve \ensuremath{\alpha}\ifmmode \tilde{}\else \~{}\fi{}(\ensuremath{\alpha}) is an incomplete devil's staircase with finite locking intervals about every rational \ensuremath{\alpha}\ifmmode \tilde{}\else \~{}\fi{}.
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