Critical and Chaotic Behaviors of Quarks

Abstract

The critical behavior of quarks undergoing phase transition to hadrons is considered in the framework of the Ising model. It is found that spatial fluctuations do not alter the F-scaling result obtained earlier in the Ginzberg-Landau formalism. For the study of chaos a new measure must be found for the quark-gluon system, for which the usual description appropriate for classical nonlinear systems is inapplicable. It is shown that the entropy indices $\mu_q$ which characterize the fluctuations of spatial patterns, are as effective as the Lyapunov exponent in measuring chaos. When applied to the QCD parton showers, it is found that the quark jets are more chaotic than gluon jets. The analysis is highly appropriate for a quantitative treatment of the erratic fluctuations of multiparticle production in leptonic, hadronic and nuclear collision processes. It represents a step beyond the traditional intermittency analysis.