The XY model is a lattice of planar spins — each pointing somewhere in a circle, interacting with neighbors, disturbed by thermal noise. In two dimensions, equilibrium theory makes a definitive prediction: quasi-long-range order survives below the Berezinskii-Kosterlitz-Thouless transition temperature, maintained by the algebraic decay of correlations. Above that temperature, disorder wins. The boundary is sharp and the noise is white — uncorrelated in time, decorrelating at every instant.
Shi, Chate, and Mahault (2602.22028) replace the white noise with persistent noise — fluctuations that remember their recent past, correlated in time. The question is natural: does temporal correlation in the noise destroy or enhance the ordered phase? Equilibrium intuition says it shouldn't matter — at long times, the noise statistics should average to their white-noise limit.
The surprising finding: quasi-long-range order survives even when noise correlations decay far more rapidly than equilibrium theory permits. The BKT transition persists, its character preserved. But the scaling exponents — the numbers that describe how correlations decay with distance — become functions of the noise persistence time. The noise isn't neutral. It actively stabilizes order.
The mechanism involves the topological defects — vortices and antivortices — that drive the BKT transition. In the equilibrium picture, these defects unbind at the critical temperature, destroying order. With persistent noise, the fluctuations that would create defects are momentarily suppressed — the noise pushes in one direction long enough to delay defect nucleation. The persistence time creates a temporal shelter for order.
This inverts a standard assumption in statistical mechanics. Noise is typically the enemy of order — it's what thermal fluctuations do. Making the noise more structured (correlated in time) should either not matter (if the system only cares about the stationary distribution) or make things worse (by pumping energy into coherent modes). Instead, the structure in the noise translates to stability in the order. The noise carries information about its own recent history, and that information protects the phase it disturbs.
The result has implications for any two-dimensional system where fluctuations aren't white. Biological membranes, active matter films, thin-film magnets — all experience correlated noise from their environments. The equilibrium BKT predictions may systematically underestimate the stability of ordered phases in these systems. The order is more robust than equilibrium theory expects because the noise is more structured than equilibrium theory assumes.
Shi, X.-q., Chate, H., & Mahault, B. (2026). XY model with persistent noise. arXiv:2602.22028.