  We study a $\mathcal PT$-symmetric scalar Euclidean field theory with a
complex action, using both theoretical analysis and lattice simulations. This
model has a rich phase structure that exhibits pattern formation in the
critical region. Analytical results and simulations associate pattern formation
with tachyonic instabilities in the homogeneous phase. Monte Carlo simulation
shows that pattern morphologies vary smoothly, without distinct microphases. We
suggest that pattern formation in this model may be regarded as a form of
arrested spinodal decomposition. We extend our theoretical analysis to
multicomponent $\mathcal PT$-symmetric Euclidean scalar field theories and show
that they give rise to new universality classes of local field theories that
exhibit patterned behavior in the critical region. QCD at finite temperature
and density is a member of the $Z(2)$ universality class when the Polyakov loop
is used to distinguish confined and deconfined phases. This suggests the
possibility of the formation of patterns of confined and deconfined matter in
QCD in the critical region in the $\mu-T$ plane.
