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arXiv · 2509.11654

Schr\"odinger-invariance in the voter model

Malte Henkel·Stoimen Stoimenov
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Abstract

Exact single-time and two-time correlations and the two-time response function are found for the order-parameter in the voter model with nearest-neighbour interactions. Their explicit dynamical scaling functions are shown to be continuous functions of the space dimension $d>0$. Their form reproduces the predictions of non-equilibrium representations of the Schr\"odinger algebra for models with dynamical exponent ${z}=2$ and with the dominant noise-source coming from the heat bath. Hence the ageing in the voter model is a paradigm for relaxations in non-equilibrium critical dynamics, without detailed balance, and with the upper critical dimension $d^*=2$.

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Malte Henkel, Stoimen Stoimenov. 2025-09-15. Schr\"odinger-invariance in the voter model. https://doi.org/10.1007/s10773-025-06151-x

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