Equation of State of the Quark-Gluon Plasma in an External Magnetic Field to Fourth Order
Abstract
We extend a lattice-QCD determination of the response of the quark-gluon plasma to an external magnetic field using a Taylor expansion of the pressure at zero field. A zero-net-flux ``half-and-half'' magnetic-field configuration permits continuous differentiation with respect to the field amplitude on gauge ensembles generated at B=0. The electromagnetic vector potential is chosen to minimize stochastic noise in the Taylor operators. Previous results through O(B2) are extended to O(B4) using 2+1-flavor HISQ/tree ensembles with ml/ms=0.05 and Nt=8. The renormalized quadratic coefficient confirms paramagnetic behavior above the QCD crossover. The fourth-order coefficient C4 is small at high temperature and is enhanced near the crossover. At T=167 MeV the C4 result at 483× 8 lies about two standard deviations above the corresponding 323×8 one, indicating likely finite- volume effects. For eB = 0.2 GeV2, characteristic of magnetic fields relevant to heavy-ion phenomenology, the fourth-order contribution is small compared with the leading magnetic correction at moderate and high temperatures, but near the crossover the large-volume result is about half of the central value of the quadratic term, after the vacuum-pressure subtraction. We also place the method in the context of other lattice determinations of magnetic susceptibility and clarify the relevance of finite-volume effects for the thermal subtraction. This work was completed in 2014 and preliminary results were reported at Lattice 2014.
Related
- Comment on "Long-range magnetic fields in the ground state of the Standard Model plasma"
- Effects of Strong Magnetic Fields on the Equation of State and Mass-Radius Structure of Hyperonic Neutron-Star Matter with Anomalous Magnetic Moments
- Integral Representations for Solutions of the Linearized Fourth Painleve Equation
- Controlling external injection in laser-plasma accelerators with terahertz frequency bunch manipulation
- What does anti-Fourier heat-flux agreement validate? Observability of the fourth-order closure state in a rarefied lid-driven cavity
BibTeX
@misc{levkova2026equation,
title = {{Equation of State of the Quark-Gluon Plasma in an External Magnetic Field to Fourth Order}},
author = {L. Levkova and C. DeTar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37799},
eprint = {2609.37799},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37799},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Equation of State of the Quark-Gluon Plasma in an External Magnetic Field to Fourth Order
AU - L. Levkova
AU - C. DeTar
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37799
UR - https://arxiv.org/abs/2609.37799
AB - We extend a lattice-QCD determination of the response of the quark-gluon plasma to an external magnetic field using a Taylor expansion of the pressure at zero field. A zero-net-flux ``half-and-half'' magnetic-field configuration permits continuous differentiation with respect to the field amplitude on gauge ensembles generated at B=0. The electromagnetic vector potential is chosen to minimize stochastic noise in the Taylor operators. Previous results through O(B^2) are extended to O(B^4) using 2+1-flavor HISQ/tree ensembles with m_l/m_s=0.05 and N_t=8. The renormalized quadratic coefficient confirms paramagnetic behavior above the QCD crossover. The fourth-order coefficient C_4 is small at high temperature and is enhanced near the crossover. At T=167 MeV the C_4 result at 48^3× 8 lies about two standard deviations above the corresponding 32^3×8 one, indicating likely finite- volume effects. For eB = 0.2 GeV^2, characteristic of magnetic fields relevant to heavy-ion phenomenology, the fourth-order contribution is small compared with the leading magnetic correction at moderate and high temperatures, but near the crossover the large-volume result is about half of the central value of the quadratic term, after the vacuum-pressure subtraction. We also place the method in the context of other lattice determinations of magnetic susceptibility and clarify the relevance of finite-volume effects for the thermal subtraction. This work was completed in 2014 and preliminary results were reported at Lattice 2014.
ER -