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An Example of Non-Existence of Plane-Like Minimizers for an Almost-Periodic Ising System

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Abstract

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 Caffarelli and de la Llave.

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Acknowledgments

The example in this paper has been constructed after a question by Matteo Novaga at a Oberwolfach Workshop on “Interplay of Analysis and Probability in Physics” in January 2012. The author gratefully acknowledges the financial support of the EPSRC Science and Innovation award to the Oxford Centre for Nonlinear PDE (EP/E035027/1).

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  1. Dipartimento di Matematica, Università di Roma Tor Vergata, via della ricerca scientifica 1, Roma, 00133, Italy

    Andrea Braides

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  1. Andrea Braides
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Correspondence to Andrea Braides.

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Braides, A. An Example of Non-Existence of Plane-Like Minimizers for an Almost-Periodic Ising System. J Stat Phys 157, 295–302 (2014). https://doi.org/10.1007/s10955-014-1069-9

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  • DOI: https://doi.org/10.1007/s10955-014-1069-9

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