  A conventional quantum phase transition (QPT) occurs not only at zero
temperature, but also exhibits finite-temperature quantum criticality.
Motivated by the discovery of the pseudo-Hermiticity of non-Hermitian systems,
we explore the finite-temperature quantum criticality in a non-Hermitian PT
-symmetric Ising model. We present the complete set of exact eigenstates of the
non-Hermitian Hamiltonian, based on which the mixed-state fidelity in the
context of biorthogonal bases is calculated. Analytical and numerical results
show that the fidelity approach to finite-temperature QPT can be extended to
the non-Hermitian Ising model. This paves the way for experimental detection of
quantum criticality in a complex-parameter plane.
