Lattice QCD with chemical potential

The Taylor Expansion
Since P V = −F = T log Z, the Taylor expansion of P is the same as of F !
1
V P (T, µ u, µ d ) = 1 V P (T, 0, 0) + ∑ f
n f µ f + 1 2!
where the quark number densities and susceptibilities are—
∑
χ fg µ f µ g + · · ·
fg
n f = T V
χ fg = T V
χ fgh··· = T V
∂ log Z
∂µ f
∣ ∣∣∣µf
=0
∣
∂ 2 log Z ∣∣∣µf
∂µ f ∂µ g =µ g =0
∂ n log Z
∣
∂µ f ∂µ g ∂µ h · · ·
∣
µf =µ g =···=0
Chemical potential/S. Gupta: IMSc, 2003 to plan, Phases, Reweight, Expansion, QNS, strangeness, EOS, masses, end 8