Six universality classes govern the critical and multicritical behavior of an active Ising model

The critical behavior of the equilibrium Ising model, famously governed by the Wilson-Fisher universality class (UC), is a cornerstone of statistical physics. A natural question is whether its properties are modified when the interacting spins are allowed to move. This can be explored within the framework of active motility by, e.g., prescribing that the spins self-propel along the direction of their orientation. In such a system, the spin number density necessarily constitutes a soft hydrodynamic mode and can therefore modify the scaling behavior. In this letter, we show that this is indeed the case in a critical active Ising model where density impedes the system's collective motion. Using a perturbative dynamic renormalization group analysis at a one-loop level, We identify six UCs, including three previously unidentified ones, one of which supersedes the Wilson-Fisher UC as the generic UC governing the critical behavior.