Electronic Journal of Probability

Spontaneous breaking of rotational symmetry in the presence of defects

Markus Heydenreich, Franz Merkl, and Silke Rolles

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We prove a strong form of spontaneous breaking of rotational symmetry for a simple model of two-dimensional crystals with random defects in thermal equilibrium at low temperature. The defects consist of isolated missing atoms.

Article information

Electron. J. Probab., Volume 19 (2014), paper no. 111, 17 pp.

Accepted: 11 December 2014
First available in Project Euclid: 4 June 2016

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs 82B21: Continuum models (systems of particles, etc.)

Spontaneous symmetry breaking localized defects rigidity estimate

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Heydenreich, Markus; Merkl, Franz; Rolles, Silke. Spontaneous breaking of rotational symmetry in the presence of defects. Electron. J. Probab. 19 (2014), paper no. 111, 17 pp. doi:10.1214/EJP.v19-2971. https://projecteuclid.org/euclid.ejp/1465065753

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