QCD matter at a finite magnetic field and nonzero chemical potential

We construct a hybrid equation of state (EoS) by smoothly interpolating the EoS in the hadron resonance gas at low temperatures to that in the ideal parton gas at high temperatures, and employ it to study the properties of the quantum chromodynamics (QCD) matter at a finite magnetic field and nonzero chemical potential. We find that dimensionless observables such as the entropy density $s/T^3$, the pressure $P/T^4$, the energy density $\varepsilon/T^4$, the trace anomaly $Δ= (\varepsilon - 3P)/T^4$, and the specific heat at constant volume $C_V/T^3$ are sensitive to both finite magnetic field and chemical potential. As the chemical potential increases from zero, these quantities rise in both the hadronic and quark-gluon plasma phases. In contrast, introducing a magnetic field suppresses them at low temperatures but enhances them at high temperatures. Furthermore, nonzero chemical potential and magnetic field introduce nontrivial modifications to the squared speed of sound $c_s^2$. Both effects increase $c_s^2$ close to the critical temperature while reducing it at lower temperatures. When the chemical potential and magnetic field are present simultaneously, their influences superimpose, leading to more intricate changes in the thermodynamic behavior. Finally, we compare our results with the lattice QCD data for the quadratic fluctuations of conserved charges and their correlations. The model successfully reproduces the temperature dependence of these observables at $eB=0$ and 0.04 GeV$^2$. However, at the stronger field strength $eB=0.14$ GeV$^2$, the model underestimates the magnitudes while still capturing the overall temperature trend.