Universality classes for percolation models with long-range correlations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909184790888448 |
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| author | Chalhoub, Christopher Drewitz, Alexander Prévost, Alexis Rodriguez, Pierre-François |
| author_facet | Chalhoub, Christopher Drewitz, Alexander Prévost, Alexis Rodriguez, Pierre-François |
| contents | We consider a class of percolation models where the local occupation variables have long-range correlations decaying as a power law $\sim r^{-a}$ at large distances $r$, for some $0< a< d$ where $d$ is the underlying spatial dimension. For several of these models, we present both, rigorous analytical results and matching simulations that determine the critical exponents characterizing the fixed point associated to their phase transition, which is of second order. The exact values we obtain are rational functions of the two parameters $a$ and $d$ alone, and do not depend on the specifics of the model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18787 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universality classes for percolation models with long-range correlations Chalhoub, Christopher Drewitz, Alexander Prévost, Alexis Rodriguez, Pierre-François Statistical Mechanics Mathematical Physics We consider a class of percolation models where the local occupation variables have long-range correlations decaying as a power law $\sim r^{-a}$ at large distances $r$, for some $0< a< d$ where $d$ is the underlying spatial dimension. For several of these models, we present both, rigorous analytical results and matching simulations that determine the critical exponents characterizing the fixed point associated to their phase transition, which is of second order. The exact values we obtain are rational functions of the two parameters $a$ and $d$ alone, and do not depend on the specifics of the model. |
| title | Universality classes for percolation models with long-range correlations |
| topic | Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2403.18787 |