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

TL;DR

This paper investigates the thermal stability of the magnetic dual chiral density wave phase in dense QCD under magnetic fields, showing it remains stable over a wide range of conditions relevant to astrophysics.

Contribution

It demonstrates that the MDCDW phase's long-range order persists at high magnetic fields and provides symmetry-based explanations for the absence of Landau-Peierls instability.

Findings

Threshold temperature near the critical temperature at high magnetic fields.

Long-range order preserved over most of the parameter space in strong magnetic fields.

Magnetic field alone does not eliminate Landau-Peierls instability in 3+1 dimensions.

Abstract

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.