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

Fuente: arXiv
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Main Authors: Braides, Andrea, Caragiulo, Fabrizio
Format: Preprint
Published: 2025
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author Braides, Andrea
Caragiulo, Fabrizio
author_facet Braides, Andrea
Caragiulo, Fabrizio
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2503_16230
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Modulated phases in Ising systems with long-range antiferromagnetic and short-range ferromagnetic interactions
Braides, Andrea
Caragiulo, Fabrizio
Analysis of PDEs
Mathematical Physics
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.
title Modulated phases in Ising systems with long-range antiferromagnetic and short-range ferromagnetic interactions
topic Analysis of PDEs
Mathematical Physics
url https://arxiv.org/abs/2503.16230