N-Midpoint Rule for Calculating the Effective Mesonic Potential at Finite Temperature

The temperature dependence of meson properties is studied by using the effective potential formalism. The effective mesonic potential is numerically calculated using the n-midpoint rule at finite temperature. The meson masses, the phase transition, and the energy density are investigated as functions of temperature. The obtained results are compared with those from other works. The present technique is compared with the Hartree approximation and the imaginary time formalism. We conclude that the calculated effective potential successfully predicts the meson properties, the phase transition, and the critical temperature in comparison with other models and avoid the difficulty that found in the Hartree approximation which depends on cutoff technique.