Non-equilibrium relaxation at a tricritical point

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Abstract
We study the purely relaxational tricritical dynamics of a non-conserved order parameter (model A) in the upper critical dimension dc=3 and in 3- epsilon dimensions. We are especially interested in the relaxation, starting from a macroscopically prepared initial state with a small correlation length. Using the methods of renormalized field theory we obtain the scaling behaviour of the correlation and response functions and study the nonlinear relaxation of the order parameter M(t). In three dimensions M(t) displays a crossover from the purely logarithmic short-time behaviour M(t) approximately (In(t/t0))-a to a t- 14 / power law with logarithmic corrections. For dimensions d<3 we obtain the exponents which govern the tricritical relaxation at lowest non-trivial order in epsilon =3-d. The dynamic scaling exponent z is calculated at second order in epsilon .