Strain Fields and Critical Phenomena in Manganites II: Spin-Lattice-Energy Hamiltonians

The dynamic critical behavior at the paramagnetic-antiferromagnetic (PM-AFM) transition in manganites has recently been studied experimentally [Niermann et al., Phys. Rev. Lett. {\bf 114}, 037204 (2015)]. We extend the Hamiltonian of Paper I by incorporating an energy field, and study the corresponding Model C of critical dynamics. We use the dynamic renormalization group (RG) approach and calculate the dynamic critical exponents $z$, $\nu z$ and the line-width exponent $\mathrm{\Delta }$ to leading order in the small expansion parameters $\epsilon =4-d+2\sigma$ and ${\epsilon }^{\mathrm{\prime }}=4-d$. Here, $d$ is the space dimension and $\sigma$ is the long-range exponent. Using $\sigma$ as an adjustable parameter, the theory gives us a good match to the experimentally available static and dynamic critical exponents at the PM-AFM transition.