Efficient energy cumulants for the Baxter–Wu model

• Janke cumulants’ scaling behavior is illustrated.
• Janke cumulants’ local minima and maxima physical importance is investigated.
• Janke cumulant effectively distinguishes phase transitions.
• Results consistent with well-known phenomenological theories.

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.