Determine the infinite-volume fourth-order magnetic response near the crossover

Determine the infinite-volume value of the fourth-order Taylor coefficient C_4 and the detailed temperature dependence of C_4 near the QCD crossover using additional spatial volumes.

Background

The half-and-half magnetic-field construction introduces surface effects whose impact appears substantially larger for the fourth-order coefficient C_4 than for the renormalized quadratic coefficient C_2r. At T=167 MeV, the results from 323×8 and 483×8 lattices differ by approximately two standard deviations, indicating possible finite-volume dependence near the crossover.

Because only two spatial volumes were studied at this temperature, the available data do not establish the thermodynamic-limit value or the detailed shape of C_4(T) in the crossover region. Resolving this issue is necessary for a controlled determination of the nonlinear magnetic contribution to the pressure.

References

Nevertheless, because only two spatial volumes are available at this temperature, these data are not sufficient to determine the infinite-volume value of $C_4$ or to establish the detailed shape of its temperature dependence near the crossover.

— 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”