Temperature chaos in directed polymers

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Original abstract

Disordered systems such as spin glasses and polymers characteristically exhibit random energy landscapes with many macroscopically separated energetic valleys corresponding to near-ground states. This high complexity renders these systems extremely sensitive to perturbations of external parameters. For instance, the support of associated Gibbs measures may change macroscopically under such perturbations, a phenomenon known as chaos in the literature. In experiments, chaotic phenomena are typically studied via temperature perturbations. In this article, we initiate the rigorous study of temperature-chaotic properties of the continuum directed random polymer (CDRP), a canonical model in the KPZ universality class. The CDRP is driven by white noise and is parametrized by inverse temperature $β$, and is known [Wu '26, Das-Zhu '24] to converge in the zero-temperature limit $β\to \infty$ to the directed landscape constructed in [Dauvergne-Ortmann-Virág '22], the putative universal scaling limit of models in the KPZ universality class. The main result of this article considers the CDRP free energies coupled through the same white noise at a pair of inverse temperatures $(β_1, β_2)$, and shows that they decouple in the limit $β_2 \gg β_1 \gg 1$, converging to a pair of independent directed landscapes. This is the first such "energetic de-correlation across temperatures" result. Our key estimate measures the "pivotality" or "influence" of spatially thin strips in models of last passage percolation. As a byproduct, the proof strategy also allows to show that the directed landscape is a two-dimensional black noise (in the sense of [Tsirelson-Vershik '98]), previously conjectured by Virág. This provides the third known example of a two-dimensional black noise after critical planar percolation [Schramm-Smirnov '11] and the Brownian web [Ellis-Feldheim '16].

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