Universality away from critical points in two-dimensional phase transitions

Abstract

The p-state clock model in two dimensions is a system of discrete rotors with a quasi-liquid phase in a region T1 < T < T2 for p > 4. We show that, for p > 4 and above a temperature Teu, all macroscopic thermal averages, such as energy or magnetization, become identical to those of the continuous rotor (p = \infty). 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 \ge 8, the collapse starts in the quasi-liquid phase and makes the transition at T2 identical to the Berezinskii-Kosterlitz-Thouless (BKT) transition of the con-tinuous rotor. For p \le 6, the transition at T2 is below Teu and no longer BKT. The results generate a comprehensive map of the critical properties at T1 and T2, and a range of experimental predictions, such as motion of magnetic domain walls, fab-rication of identical devices from different building blocks, and limits on macro-scopic distinguishability of different microscopic interactions.

1 PDF file, 4 pages, accepted for publication in Phys. Rev. Lett

References in corpus (3)

• Probability-Changing Cluster Algorithm for Potts Models
• Direct Evidence of the Discontinuous Character of the Kosterlitz-Thouless Jump
• Evidence for Kosterlitz-Thouless type orientational ordering of CF${}_3$Br monolayers physisorbed on graphite

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