  Quantum phase transitions are usually studied in terms of Hermitian
Hamiltonians. However, cold-atom experiments are intrinsically non-Hermitian
due to spontaneous decay. Here, we show that non-Hermitian systems exhibit
quantum phase transitions that are beyond the paradigm of Hermitian physics. We
consider the non-Hermitian XY model, which can be implemented using three-level
atoms with spontaneous decay. We exactly solve the model in one dimension and
show that there is a quantum phase transition from short-range order to
quasi-long-range order despite the absence of a continuous symmetry in the
Hamiltonian. The ordered phase has a frustrated spin pattern. The critical
exponent $\nu$ can be 1 or 1/2. Our results can be seen experimentally with
trapped ions, cavity QED, and atoms in optical lattices.
