The non-equilibrium critical dynamics of the Baxter model is studied through Monte Carlo simulations. The single-spin-flip stochastic dynamics is introduced on the basis of the formulation of the model as an Ising-type model on the square lattice with next-nearest-neighbor and four-spin interactions. At several points on the critical line, the dynamic critical exponent z and the critical exponent λ̄C; which characterizes the non-equilibrium critical relaxation, are estimated for the two order parameters of the model, the magnetization and the polarization. For both order parameters, the estimated λ̄c varies systematically along the critical line. On the other hand, the estimated z is almost constant. This suggests that while the exponent z is universal, the exponent λ̄c is not.
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