Quark condensate in QCD at nonzero magnetic field and temperature

Abstract

The basic form of the quark condensate for arbitrary values of external magnetic field and temperature, is derived using the field equations with account of confinement. The resulting expression of the chiral condensate is shown to be proportional to square of the singlet $q\bar q$ ground state wave function at origin, $|\phi_0(0)|^2$. For light quarks without magnetic field the condensates are proportional to $\sigma^{3/2}$ ($\sigma$ is the string tension). Numerical results are presented in 5 Tables and shown to be in good agreement with the lattice data, both for nonzero magnetic field $eB$ and temperature $T$ in the range $0 <T < 120$~MeV,~ $0 <eB <4$~GeV$^2$.