Relaxing near the critical point
Abstract
Critical slowing down of the relaxation of the order parameter has phenomenological consequences in early universe cosmology and in ultrarelativistic heavy ion collisions. We study the relaxation rate of longwavelength fluctuations of the order parameter in an O(N) scalar theory near the critical point to model the nonequilibrium dynamics of critical fluctuations near the chiral phase transition. A lowest order perturbative calculation (two loops in the coupling λ) reveals the breakdown of perturbation theory for longwavelength fluctuations in the critical region and the emergence of a hierarchy of scales with hard q>=T, semisoft T>>q>>λT and soft λT>>q loop momenta which are widely separated in the weak coupling limit. A nonperturbative resummation is implemented to leading order in the large N limit which reveals the infrared renormalization of the static scattering amplitude and the crossover to an effective three dimensional theory for the soft loop momenta near the critical point. The effective three dimensional coupling is driven to the WilsonFisher three dimensional fixed point in the soft limit. This resummation provides an infrared screening and for critical fluctuations of the order parameter with wave vectors λT>>k>>k_{us} or near the critical temperature λT>>m_{T}>>k_{us} with the ultrasoft scale k_{us}=(λT/4π)exp[4π/λ] the relaxation rate is dominated by classical semisoft loop momentum leading to Γ(k,T)=λT/(2πN). For wave vectors k<<k_{us} the damping rate is dominated by hard loop momenta and given by Γ(k,T)=4πT/[3N ln(T/k)]. Analogously, for homogeneous fluctuations in the ultracritical region m_{T}<<k_{us} the damping rate is given by Γ_{0}(m_{T},T)=4πT/[3N ln(T/m_{T})]. Thus critical slowing down emerges for ultrasoft fluctuations. In such a regime the rate is independent of the coupling λ and both perturbation theory and the classical approximation within the large N limit break down. The strong coupling regime and the shortcomings of the quasiparticle interpretation are discussed.
 Publication:

Physical Review D
 Pub Date:
 February 2001
 DOI:
 10.1103/PhysRevD.63.045007
 arXiv:
 arXiv:hepph/0004159
 Bibcode:
 2001PhRvD..63d5007B
 Keywords:

 11.10.Wx;
 11.15.Pg;
 12.38.Mh;
 64.60.Ht;
 Finitetemperature field theory;
 Expansions for large numbers of components;
 Quarkgluon plasma;
 Dynamic critical phenomena;
 High Energy Physics  Phenomenology;
 Astrophysics;
 Condensed Matter;
 High Energy Physics  Theory;
 Nuclear Theory
 EPrint:
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