Static magnetic susceptibility in finite-density SU(2) lattice gauge theory

Abstract

We study static magnetic susceptibility $\chi (T,\mu )$ in $SU(2)$ lattice gauge theory with $N_f=2$ light flavours of dynamical fermions at finite chemical potential $\mu$. Using linear response theory we find that $SU(2)$ gauge theory exhibits paramagnetic behavior in both the high-temperature deconfined regime and the low-temperature confining regime. Paramagnetic response becomes stronger at higher temperatures and larger values of the chemical potential. For our range of temperatures $0.727\le T/T_c\le 2.67$, the first coefficient of the expansion of $\chi (T,\mu )$ in even powers of $\mu /T$ around $\mu =0$ is close to that of free quarks and lies in the range $(2\dots 5)\cdot 10^{-3}$. The strongest paramagnetic response is found in the diquark condensation phase at $\mu >m_{\pi }/2$.

Comments: Contribution to the EPJA topical issue "QCD Phase Diagram in Strong Magnetic Fields", 7 pages EPJA style, 4 figures; v2: published version