Quantum fidelity and thermal phase transitions in a two-dimensional spin system

We investigate the ability of quantum fidelity in detecting the classical phase transitions (CPTs) in a two-dimensional Heisenberg-Ising mixed spin model, which has a very rich phase diagram and is exactly soluble. For a two-site subsystem of the model, the reduced fidelity (including the operator fidelity and the fidelity susceptibility) at finite temperatures is calculated, and it is found that an extreme value presents at the critical temperature, thus shows a signal for the CPTs. In some parameter region, the signal becomes blurred. We propose to use the "normalized fidelity susceptibility" to solve this problem.