Phase transition and critical properties of spin-orbital interacting systems

Phase transition and critical properties of Ising-like spin-orbital interacting systems in 2-dimensional triangular lattice are investigated. We first show that the ground state of the system is a composite spin-orbital ferro-ordered phase. Though Landau effective field theory predicts the second-order phase transition of the composite spin-orbital order, however, the critical exponents obtained by the renormalization group approach demonstrate that the spin-orbital order-disorder transition is far from the second-order, rather, it is more close to the first-order, implying that the widely observed first-order transition in many transition-metal oxides may be intrinsic. The unusual critical behavior near the transition point is attributed to the fractionalization of the composite order parameter.