  In the present work, higher-order mesonic interactions are included in the
linear sigma model at a finite temperature. The effective potential is
minimized in the calculations of the sigma and pion effective masses. The field
equations have been solved in the mean-field approximation, by using the
extended iteration method at a finite temperature. The order of chiral phase
transition, the effective sigma and pion masses, and the effective mesonic
potential are investigated as functions of the temperature. We find that the
chiral phase transition satisfies the Goldstone theorem below the critical
temperature point, when the minimization condition is satisfied in the chiral
limit. The value of the critical temperature is reduced as compared with that
of the original model in agreement with lattice QCD results. The modified model
is compared to with models in other works.
