Emergent criticality and universality class of spin and charge density wave transitions of two-component lattice Bose gases in optical cavities at finite temperature

We investigate the finite temperature spin density wave (SDW) and charge density wave (CDW) transition of two-component lattice spinor Bose gases in optical lattices in the Mott-insulator limit. At the temperature scale around half of the on-site interaction energy, we find a new critical regime emerges and features, in particular, a new bicritical line and two critical lines associated with the finite temperature SDW-CDW, homogeneous-SDW, and homogeneous-CDW transition, respectively. Direct calculation of the critical exponents for the scaling behavior and investigating on the effective theory in this critical regime show that they belong to the five-dimensional Ising universality class, clearly manifesting the long-range character of the system's interaction. Our prediction of the emergent criticality can be readily observed by current experimental setups operated at the intermediate temperature scale around half the on-site interaction energy.