Peierls Transition in Gross-Neveu Model from Bethe Ansatz

2024/04/10 by Valdemar Melin, Melin, Valdemar, Yuta Sekiguchi +5 · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions

paper · pdf · doi:10.48550/arxiv.2404.07307

openalex publication_date 2024/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The two-dimensional Gross-Neveu model is anticipated to undergo a crystalline phase transition at high baryon charge densities. This conclusion is drawn from the mean-field approximation, which closely resembles models of Peierls instability. We demonstrate that this transition indeed occurs when both the rank of the symmetry group and the dimension of the particle representation contributing to the baryon density are large (the large-N limit). We derive this result through the exact solution of the model, developing the large-N limit of the Bethe Ansatz. Our analytical construction of the large-N solution of the Bethe Ansatz equations aligns perfectly with the periodic (finite-gap) solution of the Korteweg-de Vries (KdV) of the mean-field analysis.

Cited by

• Finite-gap potentials as a semiclassical limit of the thermodynamic Bethe Ansatz
• Condensates, crystals, and renormalons in the Gross-Neveu model at finite density

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