Universality in Power-of-Two graphs

Programmable quantum simulators enable spin models with emergent geometries independent of physical locality. We investigate the critical behavior of the ``Power-of-Two" (PW2) model, which interpolates between local and treelike structures via a tunable decay $alpha$. By developing a low-energy effective field theory and utilizing the functional renormalization group, we determine the phase diagram and critical exponents. We demonstrate that $alpha$ continuously tunes the universality class, establishing the PW2 model as a novel paradigm for quantum criticality.