Renormalization group analysis of the phase transition in the critical dynamics of model E: Effect of compressibility

Critical dynamics constitutes a fascinating subject both from the ex- perimental and theoretical perspective. One of the most studied models is model E that describes critical behaviour in superfluids. Here, we consider the model in presence of additional velocity fluctuations and our main aim is to analyze possi- ble effect of compressible modes. To this end we introduce a well-known Kraichnan rapid-change model in order to generate compressible velocity ensemble. Resulting stochastic differential equations are then recast in the form of fleld-theoretic action using De Dominicis-Janssen approach. By direct power counting and analysis of ul- traviolet divergences it is shown that the model is multiplicatively renormalizable. The renormalization group equations are derived in the standard fashion and calcula- tions of universal quantities are performed to the leading order of perturbation theory in the double expansion (ϵ, θ) scheme. Here, ϵ is the deviation from upper critical dimension 4 and θ is the deviation from the Kolmogorov scaling regime. The fixed points of the renormalization group are given and possible infrared stable regimes are discussed in detail.