Discrete double-porosity models for spin systems

2015/12/01 by Braides Andrea, Andrea Braides, Andrea, Braides +5 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #35Q82 #39A12 #39A70 #49M25 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Theoretical and Computational Physics #math.AP #msc:35Q82 #msc:39A12 #msc:39A70 #msc:49M25

paper · pdf · doi:10.48550/arxiv.1512.00317

arXiv admin note: text overlap with arXiv:1406.1752

arxiv created 2015/12/01 · openalex publication_date 2015/12/01 · arxiv updated 2015/12/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We consider spin systems between a finite number N of "species" or "phases" partitioning a cubic lattice 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.

Citations

• Discrete double-porosity models

Cited by

• Interfaces, Modulated Phases and Textures in Lattice Systems

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