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 T14. 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> or =8, the collapse starts in the quasiliquid phase and makes the transition at T2 identical to the Berezinskii-Kosterlitz-Thouless (BKT) transition of the continuous rotor. For p< or =6, the transition at T2 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.