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arXiv · 1310.4084

Q-tensor continuum energies as limits of head-to-tail-symmetric spin systems

Andrea Braides·Marco Cicalese·Francesco Solombrino
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Abstract

We consider a class of spin-type discrete systems and analyze their continuum limit as the lattice spacing goes to zero. Under standard coerciveness and growth assumptions together with an additional head-to-tail symmetry condition, we observe that this limit can be conveniently written as a functional in the space of $Q$-tensors. We further characterize the limit energy density in several cases (both in 2 and 3 dimensions). In the planar case we also develop a second-order theory and we derive gradient or concentration-type models according to the chosen scaling.

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Andrea Braides, Marco Cicalese, Francesco Solombrino. 2013-10-15. Q-tensor continuum energies as limits of head-to-tail-symmetric spin systems. https://arxiv.org/abs/1310.4084

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