Phase Transitions in a spin-orbital model for the Iron Pnictides

We study the finite temperature phase transition of a spin-orbital Hamiltonian (arXiv:09034408) that could describe the striped magnetic order in the Iron Pnictide materials. The model consists of an Ising like orbital variable with a classical Heisenberg spin variable on a 2D square lattice. The exchange constants for the Heisenberg spins depend on the Ising variables and lead to a strong coupling between spins and orbitals. We use a Monte Carlo algorithm with feedback parallel tempering to study the phase transition. In the model, the orbital phase transition occurs at $T_c=0.447J$ with critical exponents $\nu =1.01 \pm .02$ amd $\gamma =1.74 \pm .03$ consistent with the Ising universality $^{[1]}$. We characterize the heat capacity and orbital susceptibility for the system and study magnetic properties of the system at $\vec q = 0$ and at the ordering wave vector. \\[4pt] [1] C.-C. Chen et al. Phys Rev B 80, 180418 (R), (2009)