Competing interactions in a long-range spin-lattice coupled model and tricriticality

The interplay of spin and lattice degrees of freedom on the critical behavior of magnetic phase transitions in strongly correlated systems can be studied analytically by constructing an effective model Hamiltonian for the corresponding order parameters. Here we consider such a model C-type Hamiltonian involving the coupling between order parameter and the strain field. Taking the strain interaction to be long-range (LR) in nature, we carry out a renormalization-group analysis at one-loop order. This reveals a non-trivial critical behavior dictated by an LR fixed point. We show that the critical behavior differs in the presence of competing short-range interaction. For the case of purely nonlocal theory, we find a signature of first-order instability at the leading order of the perturbation expansion. We also discuss briefly the applicability of the model in capturing the experimental results.