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 $0.727 \leq T/T_c \leq 2.67$, 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 $(2 \ldots 5) \cdot 10^{-3}$. The strongest paramagnetic response is found in the diquark condensation phase at $\mu > m_{\pi}/2$.