Spin susceptibility of degenerate quark matter

TL;DR

This paper derives the spin susceptibility of degenerate quark matter including corrections up to order g^4 log g^2, revealing a ferromagnetic phase transition at low density and analyzing related thermodynamic properties.

Contribution

It provides a detailed calculation of spin susceptibility with higher-order corrections and explores the phase transition and thermodynamic properties of polarized quark matter.

Findings

Spin susceptibility changes sign at low density, indicating ferromagnetic transition.

Polarized matter has a stiffer equation of state than unpolarized matter.

Finite temperature corrections to exchange energy are derived.

Abstract

The expression for the spin susceptibility $\chi$ of degenerate quark matter is derived with corrections upto $ {\cal O}(g^4\ln g^2)$. It is shown that at low density, $\chi^{-1}$ changes sign and turns negative indicating a ferromagnetic phase transition. To this order, we also calculate sound velocity $c_1$ and incompressibility $K$ with arbitrary spin polarization. The estimated values of $c_1$ and $K$ show that the equation of state of the polarized matter is stiffer than the unpolarized one. Finally we determine the finite temperature corrections to the exchange energy and derive corresponding results for the spin susceptibility.