Universality away from critical points in two-dimensional phase transitions

The p-state clock model in two dimensions is a system of discrete rotors with a quasiliquid phase in a region T-1 < T < T-2 for p > 4. We show that, for p > 4 and above a temperature T-eu, all macroscopic thermal averages become identical to those of the continuous rotor (p=infinity). This collapse of thermodynamic observables creates a regime of extended universality in the phase diagram and an emergent symmetry, not present in the Hamiltonian. For p >= 8, the collapse starts in the quasiliquid phase and makes the transition at T-2 identical to the Berezinskii-Kosterlitz-Thouless (BKT) transition of the continuous rotor. For p <= 6, the transition at T-2 is below T-eu and no longer a BKT transition. The results generate a range of experimental predictions, such as the motion of magnetic domain walls, and limits on macroscopic distinguishability of different microscopic interactions.