Published Paper
Inserted: 1 dec 2015
Last Updated: 2 jul 2016
Journal: Math. Mech. Complex Syst.
Volume: 4
Pages: 79-102
Year: 2016
Doi: 10.2140/memocs.2016.4.79
Abstract:
We consider spin systems between a finite number $N$ of ``species'' or ``phases'' partitioning a cubic lattice $\mathbb{Z}^d$. We suppose that interactions between points of the same phase are coercive, while between point of different phases (or, possibly, between points of an additional ``weak phase'') are of lower order. Following a discrete-to-continuum approach we characterize the limit as a continuum energy defined on $N$-tuples of sets (corresponding to the $N$ strong phases) composed of a surface part, taking into account homogenization at the interface of each strong phase, and a bulk part which describes the combined effect of lower-order terms, weak interactions between phases, and possible oscillations in the weak phase.
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