Critical dynamics of a nonlocal model and critical behavior of perovskite manganites

We investigate the nonconserved critical dynamics of a nonlocal model Hamiltonian incorporating screened long-range interactions in the quartic term. Employing dynamic renormalization group analysis at one-loop order, we calculate the dynamic critical exponent $z=2+\epsilon f_1(\sigma ,\kappa ,n)+O\left({\epsilon }^2\right)$ and the linewidth exponent $w=-\sigma +\epsilon f_2(\sigma ,\kappa ,n)+O\left({\epsilon }^2\right)$ in the leading order of $\epsilon$, where $\epsilon =4-d+2\sigma$, with $d$ the space dimension, $n$ the number of components in the order parameter, and $\sigma$ and $\kappa$ the parameters coming from the nonlocal interaction term. The resulting values of linewidth exponent $w$ for a wide range of $\sigma$ is found to be in good agreement with the existing experimental estimates from spin relaxation measurements in perovskite manganite samples.

Figure 1

One-loop Feynman diagrams corresponding to the self-energies (a) ${\mathrm{\Sigma }}_a$ and (b) ${\mathrm{\Sigma }}_b$. Solid lines represent the propagator $G_0$, dashed lines the field ${\varphi }_i$, dots the noise correlation, and wiggly lines represent the nonlocal coupling $u\left(\mathbf{k}\right)$.

Figure 2

One-loop Feynman diagrams for the vertex $u({\mathbf{k}}_1-\mathbf{k})$. Panels (a), (b), and (c) correspond to ${\mathrm{{\rm Y}}}_a, {\mathrm{{\rm Y}}}_b$, and ${\mathrm{{\rm Y}}}_c$ given in Eqs. (13, 14, 15). The various lines and the dots have the same meanings as in Fig. 1.

Figure 3

Plots for $z=2+\epsilon f_1(\sigma ,\kappa ,n)+O\left({\epsilon }^2\right)$. Panel (a) shows the variation of $z$ with $n$ for $\kappa =0.001$ and panel (b) shows the variation of $z$ with $\kappa$ for $n=3$ in $d=3$. The dotted, dashed, and solid curves correspond to $n=1,2,3$ in (a) and $\kappa =0.0001,0.001,0.01$ in (b).

Figure 4

Plots for $w=-\sigma +\epsilon f_2(\sigma ,\kappa ,n)+O\left({\epsilon }^2\right)$. Panel (a) shows the variation of $w$ with $n$ for $\kappa =0.001$ and panel (b) shows the variation of $w$ with $\kappa$ for $n=3$ in $d=3$. The dotted, dashed, and solid curves correspond to $n=1,2,3$ in (a) and $\kappa =0.0001,0.001,0.01$ in (b).