Functional renormalization group approach to the dynamics of first-order phase transitions

We apply the functional renormalization group theory to the dynamics of first-order phase transitions and show that a potential with all odd-order terms can describe spinodal decomposition phenomena. We derive a momentum-dependent dynamic flow equation which is decoupled from the static flow equation. We find the expected instability fixed points; and their associated exponents agree remarkably with the existent theoretical and numerical results. The complex renormalization group flows are found and their properties are shown. Both the exponents and the complex flows show that the spinodal decomposition possesses singularity with consequent scaling and universality.