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Optimal bounds for periodic mixtures of nearest-neighbour ferromagnetic interactions. (English) Zbl 1373.35029

The authors study the homogenization of a two-dimensional lattice, where the grid points are seen as a mixture of two types of particles involved in nearest-neighbour interactions. This is supposed to mimic ferromagnetic interactions in a planar system of a mixture of spins. As main tool, one uses the concept of \(\Gamma\)-convergence to characterize the limit energies in a discrete-to-continuum setting.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
39A12 Discrete version of topics in analysis
74Q20 Bounds on effective properties in solid mechanics
74E30 Composite and mixture properties
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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