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arXiv · 2503.16230

Modulated phases in Ising systems with long-range antiferromagnetic and short-range ferromagnetic interactions

Andrea Braides·Fabrizio Caragiulo
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Abstract

We consider large spin systems with short-range ferromagnetic interactions and long-range antiferromagnetic interactions subjected to periodic boundary conditions which have been proved by Giuliani, Lebowitz and Lieb to have minimizers that tend to alternate groups of $1$ and $-1$ of the same length $h^\star$. We consider states with energy of the same order as that of minimizers and show that they consist of a finite number of modulated phases of the same form as minimizers with some interfacial defects. The analysis is carried out using the notation of Gamma-convergence by exhibiting an interfacial energy that describes the minimal defect energy between different modulated phases.

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Andrea Braides, Fabrizio Caragiulo. 2025-03-20. Modulated phases in Ising systems with long-range antiferromagnetic and short-range ferromagnetic interactions. https://arxiv.org/abs/2503.16230

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