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arXiv · 2312.16372

Convergence of Ginzburg-Landau expansions: superconductivity in the Bardeen-Cooper-Schrieffer theory and chiral symmetry breaking in the Nambu-Jona-Lasinio model

William Gyory·Naoki Yamamoto
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Abstract

We study the convergence of the Ginzburg-Landau (GL) expansion in the context of the Bardeen-Cooper-Schrieffer (BCS) theory for superconductivity and the Nambu-Jona-Lasinio (NJL) model for chiral symmetry breaking at finite temperature $T$ and chemical potential $μ$. We present derivations of the all-order formulas for the coefficients of the GL expansions in both systems under the mean-field approximation. We show that the convergence radii for the BCS gap $Δ$ and dynamical quark mass $M$ are given by $Δ_\text{conv} = πT$ and $M_\text{conv} = \sqrt{μ^2 + (πT)^2}$, respectively. We also discuss the implications of these results and the quantitative reliability of the GL expansion near the first-order chiral phase transition.

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William Gyory, Naoki Yamamoto. 2024-04-09. Convergence of Ginzburg-Landau expansions: superconductivity in the Bardeen-Cooper-Schrieffer theory and chiral symmetry breaking in the Nambu-Jona-Lasinio model. https://doi.org/10.1093/ptep%2Fptae032

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