The Berezinskii-Kosterlitz-Thouless transition is one of the most elegant results in statistical physics. In a 2D XY model — spins on a lattice, each pointing in some direction on a circle — there's a transition from a quasi-ordered state (algebraic correlations, bound vortex-antivortex pairs) to a disordered state (free vortices, exponential decay). The transition is topological: it's about the unbinding of defects, not the breaking of symmetry.
This transition exists in equilibrium. Thermal fluctuations satisfy detailed balance. The noise is white, uncorrelated, the kind of noise that statistics textbooks are built on. What happens when the noise is persistent — correlated in time, the way active matter systems actually behave?
Shi, Chaté, and Mahault (arXiv:2602.22028) answer this: the BKT transition survives. A 2D XY model driven by time-correlated noise — noise with memory, noise that pushes in the same direction for a while before switching — still exhibits quasi-long-range order at low noise and a vortex-unbinding transition to disorder at high noise. The topological structure is inherited from equilibrium even though the system is not in equilibrium.
The inheritance is not exact. The scaling exponents vary with the persistence time of the noise. Longer correlations change the quantitative details of how order decays with distance. But the qualitative structure — bound vortices below the transition, free vortices above, algebraic correlations in between — remains intact. The topology is robust to the violation of detailed balance.
This matters for active crystals — dense suspensions of self-propelled particles that form ordered lattices. These systems have persistent noise by construction: each particle has a propulsion direction that changes slowly compared to the collision timescale. If the BKT framework extends to active crystals, then the same theoretical machinery developed for superfluid helium films and 2D melting applies to bacterial colonies and vibrated granular media. Not metaphorically. Quantitatively.
The deeper question is why topological transitions are so robust. Symmetry breaking is fragile — change the noise statistics and you change the order parameter behavior. But vortex unbinding depends on the energy cost of isolated defects versus the entropy of placing them, and this balance is less sensitive to how the fluctuations are generated. Topology cares about what the defects are, not about how they got there.
Based on X. Shi, H. Chaté, and B. Mahault, "XY Model with Persistent Noise" (arXiv:2602.22028, February 2026).