Long range to short range crossover in one dimension
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913937932419072 |
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| author | Sarkar, Mrinal Defenu, Nicolò Enss, Tilman |
| author_facet | Sarkar, Mrinal Defenu, Nicolò Enss, Tilman |
| contents | This work investigates the critical behavior of one-dimensional systems with long-range (LR) interactions, focusing on the crossover to short-range (SR) universality. Through large-scale Monte Carlo simulations of self-avoiding Lévy flights on a 1D lattice, we compute the anomalous dimension η, the correlation length exponent ν, and the susceptibility exponent γacross a wide range of LR decay parameters σ. Our results provide strong numerical evidence that supports Sak's scenario. They identify the crossover at σ^* = 1 and demonstrate the continuity of critical exponents across this point, with strong corrections to scaling. The study also reveals deviations from Flory-type scaling predictions and discusses the limitations of effective dimension approaches in general. These findings clarify the nature of the LR-SR crossover in low-dimensional systems and open avenues for exploring criticality in disordered and complex networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08092 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Long range to short range crossover in one dimension Sarkar, Mrinal Defenu, Nicolò Enss, Tilman Statistical Mechanics This work investigates the critical behavior of one-dimensional systems with long-range (LR) interactions, focusing on the crossover to short-range (SR) universality. Through large-scale Monte Carlo simulations of self-avoiding Lévy flights on a 1D lattice, we compute the anomalous dimension η, the correlation length exponent ν, and the susceptibility exponent γacross a wide range of LR decay parameters σ. Our results provide strong numerical evidence that supports Sak's scenario. They identify the crossover at σ^* = 1 and demonstrate the continuity of critical exponents across this point, with strong corrections to scaling. The study also reveals deviations from Flory-type scaling predictions and discusses the limitations of effective dimension approaches in general. These findings clarify the nature of the LR-SR crossover in low-dimensional systems and open avenues for exploring criticality in disordered and complex networks. |
| title | Long range to short range crossover in one dimension |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2507.08092 |