Universality away from critical points in two-dimensional phase transitions

TL;DR

This paper demonstrates that in two-dimensional p-state clock models with p > 4, thermodynamic properties become indistinguishable from the continuous rotor model above a certain temperature, revealing an extended universality regime.

Contribution

It uncovers a regime of extended universality in 2D clock models where macroscopic averages match the continuous rotor, and maps critical properties across different p values.

Findings

Thermodynamic averages collapse to continuous rotor values above Teu for p > 4.

Transition at T2 becomes identical to BKT transition for p ≥ 8.

No BKT transition at T2 for p ≤ 6.

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.