Relaxing near the critical point - art. no. 045007

Critical slowing down of the relaxation of the order parameter has phenomen ological consequences in early universe cosmology and in ultrarelativistic heavy ion collisions, We study the relaxation rate of long-wavelength fluct uations of the order parameter in an O(N) scalar theory near the critical p oint to model the non-equilibrium dynamics of critical fluctuations near th e chiral phase transition. A lowest order perturbative calculation (two loo ps in the coupling lambda) reveals the breakdown of perturbation theory for long-wavelength fluctuations in the critical region and the emergence of a hierarchy of scales with hard q greater than or equal toT, semisoft T much greater thanq much greater than lambdaT and soft lambdaT much greater than q loop momenta which are widely separated in the weak coupling limit, A non -perturbative resummation is implemented to leading order in the large N li mit which reveals the infrared renormalization of the static scattering amp litude and the crossover to an effective three dimensional theory for the s oft loop momenta near the critical point. The effective three dimensional c oupling is driven to the Wilson-Fisher three dimensional fixed point in the soft limit. This resummation provides an infrared screening and for critic al fluctuations of the order parameter with wave vectors lambdaT much great er thank much greater thank(us), or near the critical temperature lambdaT m uch greater thanm(T)much greater thank(us) with the ultrasoft scale k(us) = (lambdaT/4 pi )exp[-4 pi/lambda] the relaxation rate is dominated by class ical semisoft loop momentum leading to Gamma (k,T) = lambdaT/(2 piN). For w ave vectors k much less thank(us) the damping rate is dominated by hard loo p momenta and given by Gamma (k, T) = 4 piT/[3N ln(T/k)]. Analogously, for homogeneous fluctuations in the ultracritical region m(T)much less thank(us ) the damping rate is given by Gamma (0)(m(T),T) = 4 piT/[3N ln(T/m(T))]. T hus critical slowing down emerges for ultrasoft fluctuations. In such a reg ime the rate is independent of the coupling lambda and both perturbation th eory and the classical approximation within the large N limit break down. T he strong coupling regime and the shortcomings of the quasiparticle interpr etation are discussed.