Phase ordering from off-critical quenches and the measurement of the dynamic exponent lambda

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Abstract
The ordering dynamics of a system with a nonconserved order parameter is considered following a quench into the ordered phase from high temperature. The correlation of the order-parameter field with its initial condition (or, more generally, the correlation between the fields at different times) involves the dynamic exponent lambda , a non-trivial exponent associated with the T=0 fixed point that drives phase ordering. It is shown that lambda can be determined from the growth of the mean order parameter m(t) in a system which has a small but non-zero mean order parameter m0 at t=0, since m(t) approximately m0L(t)lambda where L(t) approximately t1/2 is the characteristic length scale at time t. The role of a weak external field h is also considered: for h not=0 the growth of m(t) involves two power-law terms, m(t) approximately h(at3+btlambda/2 ) for (m0=0), with x=1/2 or 1 for a scalar or vector order parameter, respectively. The results are illustrated by the exact solution of the O(n) model at large n for general values of m0 and h.