Thermal phonon fluctuations and stability of the magnetic dual chiral density wave phase in dense QCD

• Published in: arXiv.org 2024-03
• Main Authors: Ferrer, E J, Gyory, W, de la Incera, V
• Format: Article
• Language: English
• Subjects: Critical temperature; Density; Long range order; Magnetic fields; Parameters; Phonons; Stability; Transition temperature
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2307.05621

We study the stability against thermal phonon fluctuations of the magnetic dual chiral density wave (MDCDW) phase, an inhomogeneous phase arising in cold dense QCD in a magnetic field. Following a recent study that demonstrated the absence of the Landau-Peierls (LP) instability from this phase, we calculate the (threshold) temperature at which the phonon fluctuations wash out the long-range order over a range of magnetic fields and densities relevant to astrophysical applications. Using a high-order Ginzburg-Landau expansion, we find that the threshold temperature is very near the critical temperature for fields of order \(10^{18}\) G, and still a sizable fraction of the critical temperature for fields of order \(10^{17}\) G. Therefore, at sufficiently large magnetic fields, the long-range order of the MDCDW phase is preserved over most of the parameter space where it is energetically favored; at smaller magnetic fields, the long-range order is still preserved over a considerable region of parameter space relevant to compact stars. We provide general symmetry arguments to explain why a magnetic field alone is not enough to eliminate the LP instability that characterizes single-modulated phases in 3+1 dimensions.