Dynamic Universality Class of Model H with Frustrated Diffusion: $ϵ$-Expansion

Abstract

We study a variation of the dynamic universality class of model H in a spatial dimension of $d=4-ϵ$, by frustrating charge diffusion and momentum density fluctuations along $d_T=1$ or $d_T=2$ dimensions, while keeping the same dynamics of model H in the other $d_L=d-d_T$ dimensions. The case of $d_T=2$ describes the QCD critical point in a background magnetic field. We find that these models belong to a different dynamical universality class due to extended conservation laws compared to the model H, although the static universality class remains the same as the 3-dimensional Ising model. We compute the dynamic critical exponents of these models in first order of $ϵ$-expansion to find that $x_{\lambda }\approx 0.847ϵ$, $x_{\bar{\eta }}\approx 0.153ϵ$, and $z=4-x_{\lambda }\approx 3.15$ when $ϵ=1$ and $d_T=2$. For $d_T=1$ the results are numerically similar to the model H values: $z\approx 3.08$.

Comments: 15 pages, 3 figures