Efficient energy cumulants for the Baxter–Wu model

In this paper, using both analytic methods and Monte Carlo simulations with our triangle cluster algorithm, we illustrate the scaling behavior of two possible 4th-order connected energy cumulants across the well-known second and first-order phase transitions of the Baxter–Wu model under zero external magnetic field. It is found that 4th-order connected energy cumulant introduced by Janke provides a very good theoretical tool for finding and distinguishing phase transitions, especially in case the order parameter of a particular model is hardly known. Also, the physical importance of the cumulants’ local minima and maxima is investigated, showing that they are finite-size scaling effects.