Origin of the cumulant-crossing drift

Determine whether the observed drift of the fourth-order cumulant $U_Q$ at successive finite-size crossing temperatures is caused by genuine corrections to scaling or by the instability of the field-mixing parameter $s_L$ in the honeycomb-lattice Blume–Capel analysis.

Background

At the tricritical point, the fourth-order cumulant $U_Q$ is expected to approach a universal value, quoted in the paper as approximately $0.571$. The authors examine crossings of cumulant curves for successive lattice sizes as a consistency test of tricritical scaling.

Instead of approaching the expected value monotonically or remaining stable, the crossing values drift from $0.563$ for the $12\times16$ pair to $0.534$ for the $36\times48$ pair. The paper notes that the field-mixing parameter $s_L$ becomes increasingly difficult to determine because the equal-height condition loses sensitivity at large sizes, leaving unresolved whether the drift is physical or methodological.