2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/204053The relationship between quantum phase transition and complex geometric phase for open quantum system governed by the non-Hermitian effective Hamiltonian with the accidental crossing of the eigenvalues is established. In particular, the geometric phase associated with the ground state of the one-dimensional dissipative Ising model in a transverse magnetic field is evaluated, and it is demonstrated that related quantum phase transition is of the first order.ReVTeX style, 6 figures. Accepted for publication in Phys. Rev. E (Rapid Communication)Quantum PhysicsHigh Energy Physics - TheoryMathematical Physicstext