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 Hamiltonian of Paper I by incorporating an energy field, and study corresponding Model C dynamics. use renormalization group (RG) approach calculate exponents $z$, $\nu z$ line-width exponent $\Delta$ to leading order small expansion parameters $\epsilon=4-d+2\sigma$ $\epsilon'=4-d$. Here, $d$ is space dimension $\sigma$ long-range exponent. Using as adjustable parameter, theory gives us a good match available static PM-AFM transition.