Novel first-order phase transition and critical points in SU(3) Yang-Mills theory with spatial compactification

We investigate the thermodynamics and phase structure of $SU(3)$ Yang-Mills theory on ${\mathbb{T}}^2\times {\mathbb{R}}^2$ in Euclidean spacetime in an effective-model approach. The model incorporates two Polyakov loops along two compactified directions as dynamical variables, and is constructed to reproduce thermodynamics on ${\mathbb{T}}^2\times {\mathbb{R}}^2$ measured on the lattice. The model analysis indicates the existence of a novel first-order phase transition on ${\mathbb{T}}^2\times {\mathbb{R}}^2$ in the deconfined phase, which terminates at critical points that should belong to the two-dimensional $Z_2$ universality class. We argue that the interplay of the Polyakov loops induced by their cross term in the Polyakov-loop potential is responsible for the manifestation of the first-order transition.