Discrete spin systems on random lattices at the bulk scaling

Marco Cicalese; Matthias Ruf

doi:10.3934/dcdss.2017006

Article Contents

2017, Volume 10, Issue 1: 101-117. Doi: 10.3934/dcdss.2017006

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Discrete spin systems on random lattices at the bulk scaling

Marco Cicalese and
Matthias Ruf

Zentrum Mathematik -M7, Technische Universität München, Boltzmannstrasse 3, 85748 Garching, Germany

Author Bio: E-mail address: cicalese@ma.tum.de; E-mail address: mruf@ma.tum.de

Received: March 2015

Revised: June 2015

Published: February 2018

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Abstract

We study by Γ-convergence the stochastic homogenization of discrete energies on a class of random lattices as the lattice spacing vanishes. We consider general bounded spin systems at the bulk scaling and prove a homogenization result for stationary lattices. In the ergodic case we obtain a deterministic limit.

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Mathematics Subject Classification: Primary: 49J45, 49J55, 82B20; Secondary: 49S05.

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References

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