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We investigate the finite temperature spin density wave (SDW) and chargedensity wave (CDW) transition of two-component lattice spinor Bose gases inoptical lattices in the Mott-insulator limit. At the temperature scale aroundhalf of the on-site interaction energy, we find a new critical regime emergesand features, in particular, a new bicritical line and two critical linesassociated with the finite temperature SDW-CDW, homogeneous-SDW, andhomogeneous-CDW transition, respectively. Direct calculation of the criticalexponents for the scaling behavior and investigating on the effective theory inthis critical regime show that they belong to the five-dimensional Isinguniversality class, clearly manifesting the long-range character of thesystem's interaction. Our prediction of the emergent criticality can be readilyobserved by current experimental setups operated at the intermediatetemperature scale around half the on-site interaction energy.

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