Generalized susceptibilities along the phase boundary of the three-dimensional, three-state Potts model

Through the Monte Carlo simulation of the three-dimensional, three-state Potts model, which is a paradigm of finite-temperature pure gauge quantum chromodynamics, we study the fluctuations of generalized susceptibilities near the temperatures of external fields of first- and second-order phase transitions and crossover. Similar peak-like fluctuation appears in the second-order susceptibility at three given external fields. Oscillation-like fluctuation appears in the third-to sixth-order susceptibilities. We find that these non-monotonic fluctuations are not only associated with the second-order phase transition, but also the first-order one and crossover in a system of finite size. We further present the finite-size scaling analysis of the second- and fourth-order susceptibilities. The exponent of the scaling characterizes the order of the transitions, or the crossover.