Spin susceptibility of degenerate quark matter

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.