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An example of non-existence of plane-like minimizers for an almost-periodic Ising system. (English) Zbl 1302.82015
Summary: We give an example of a ferromagnetic spin system with uniformly almost-periodic coefficients whose ground states may not be confined in any finite strip, in contrast to what previously proved in the case of periodic coefficients by L. A. Caffarelli and R. de la Llave [J. Stat. Phys. 118, No. 3–4, 687–719 (2005; Zbl 1126.82305)].

MSC:
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82D40 Statistical mechanics of magnetic materials
49Q05 Minimal surfaces and optimization
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