We analyze the simplest model of identical coupled phase oscillators subject
to two-body and three-body interactions with permutation symmetry. This model
is derived from an ensemble of weakly coupled nonlinear oscillators by phase
reduction. Our study indicates that higher-order interactions induce anomalous
transitions to synchrony. Unlike the conventional Kuramoto model, higher-order
interactions lead to anomalous phenomena such as multistability of full
synchronization, incoherent, and two-cluster states, and transitions to
synchrony through slow switching and clustering. Phase diagrams of the
dynamical regimes are constructed theoretically and verified by direct
numerical simulations. We also show that similar transition scenarios are
observed even if a small heterogeneity in the oscillators' frequency is
included