Ground state energy of spin polarized quark matter with correlation

TL;DR

This paper calculates the ground state energy of spin polarized quark matter, including correlation effects, and explores the conditions for ferromagnetic phase transition at low densities.

Contribution

It derives expressions for correlation energy in both non-relativistic and ultra-relativistic regimes and analyzes their impact on ferromagnetic phase transition.

Findings

Correlation energy does not prevent ferromagnetic transition at low density.

Expressions for correlation energy in different regimes are provided.

Spin stiffness constant is derived for high-density spin polarized matter.

Abstract

We calculate the ground state energy of cold and dense spin polarized quark matter with corrections due to correlation energy $(E_{corr})$. Expressions for $E_{corr}$ both in the non-relativistic and ultra-relativistic regimes have been derived and compared with the exchange and kinetic term present in the perturbation series. It is observed that the inclusion of correlation energy does not rule out the possibility of the ferromagnetic phase transition at low density within the model proposed by Tatsumi\cite{tatsumi00}. We also derive the spin stiffness constant in the high density limit of such a spin polarized matter.