Non-Hermitian Ising model at finite temperature

As a very simple model,the Ising model plays an important role in statistical physics.In the paper,with the help of quantum Liouvillian statistical theory,we study the one-dimensional nonHermitian Ising model at finite temperature and give its analytical solutions.We find that the nonHermitian Ising model shows quite different properties from those of its Hermitian counterpart.For example,the‘pseudo-phase transition’is explored between the‘topological’phase and the‘nontopological’phase,at which the Liouvillian energy gap is closed rather than the usual energy gap.In particular,we point out that the one-dimensional non-Hermitian Ising model at finite temperature can be equivalent to an effective anisotropic XY model in the transverse field.This work will help people understand quantum statistical properties of non-Hermitian systems at finite temperatures.