The order of the thermal chiral phase transition in lattice QCD is strongly cutoff-dependent.
A recent study from our group using mass-degenerate, unimproved staggered quarks on
$N_\tau\in\left\{4,6,8\right\}$ lattices found that the first-order regions shrink to zero
for $N_\mathrm{f}\in\left[2,6\right]$ as the continuum limit is approached for zero chemical
potential [Cuteri et al. 10.1007/JHEP11(2021)141].
Here we present the progress of an analogous study at a fixed value of imaginary baryon chemical
potential of $\mu_i=0.81\frac{\pi T}{3}$.
The same qualitative behavior as for zero chemical potential is found:
The first-order regions are bounded by $Z_2$-critical lines which exhibit tricritical
scaling for sufficiently small quark masses and
disappear with decreasing lattice spacing in tricritical points.
The results suggest a second order chiral phase transition in the continuum limit for
$N_\mathrm{f}\in\left[2,6\right]$ for both cases, at zero and imaginary chemical potential.
Additionally an effective Ginzburg-Landau theory is developed around the tricritical point in
the chiral limit.
The possibility to describe the lattice phase structure by the Ginzburg-Landau potential
is explored.