Establish whether fourth-order finite-volume effects cancel in the thermal subtraction

Determine whether the enhanced finite-volume effects in the half-and-half fourth-order coefficient C_4 cancel substantially between finite-temperature and zero-temperature calculations in the renormalized thermal combination C_4^r(T,L)=C_4(T,L)-C_4(0,L).

Background

The reported C_4 values were not zero-temperature subtracted, unlike the renormalized quadratic coefficient C_2r. The larger finite-volume dependence observed for C_4 could arise from vacuum or surface contributions associated with the discontinuous half-and-half magnetic-field profile.

A matched zero-temperature calculation on the 323 and 483 volumes at β=6.423 would test whether these effects cancel in the thermal subtraction. Such a calculation would distinguish predominantly vacuum or surface artifacts from genuine finite-volume dependence of the thermal nonlinear magnetic response.

References

Whether such a cancellation occurs at fourth order cannot be determined from the present data, since the required zero-temperature $C_4$ measurements were not performed.

— Equation of State of the Quark-Gluon Plasma in an External Magnetic Field to Fourth Order  (2609.37799 - Levkova et al., 29 Sep 2026) in Section 5.2, subsection “Fourth-order response”