Schrödinger-invariance in the voter model
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912892657336320 |
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| author | Henkel, Malte Stoimenov, Stoimen |
| author_facet | Henkel, Malte Stoimenov, Stoimen |
| contents | 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 Schrödinger 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 $d^*=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11654 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Schrödinger-invariance in the voter model Henkel, Malte Stoimenov, Stoimen Statistical Mechanics High Energy Physics - Theory Mathematical Physics 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 Schrödinger 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 $d^*=2$. |
| title | Schrödinger-invariance in the voter model |
| topic | Statistical Mechanics High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2509.11654 |