# Absence of Landau-Peierls Instability in the Magnetic Dual Chiral Density Wave Phase of Dense QCD

## TL;DR

This paper demonstrates that the Magnetic Dual Chiral Density Wave phase of dense QCD remains stable at finite temperature due to the absence of Landau-Peierls instabilities, influenced by magnetic field effects.

## Contribution

It reveals the stability of the MDCDW phase against fluctuations, highlighting the role of magnetic fields and symmetry breaking in preventing typical instabilities.

## Key findings

- Long-range order persists at finite temperature.
- Absence of transverse soft modes in fluctuation spectrum.
- Stability implications for neutron star physics.

## Abstract

We investigate the stability of the Magnetic Dual Chiral Density Wave (MDCDW) phase of cold and dense QCD against collective low-energy fluctuations of the order parameter. The appearance of additional structures in the system free-energy due to the explicit breaking of the rotational and isospin symmetries by the external magnetic field and the field-induced asymmetry of the lowest Landau level modes play a crucial role in the analysis. The new structures not only affect the condensate minimum equations, but also the spectrum of the thermal fluctuations, which lacks the transverse soft modes that typically affect single-modulated inhomogeneous phases in the absence of a magnetic field. Consequently, the long-range order of the MDCDW phase is preserved at finite temperature. The lack of Landau-Peierls instabilities in the MDCDW phase makes this inhomogeneous phase of dense quark matter particularly relevant for the physics of neutron stars.