Logarithmic correlation functions in 2D critical percolation
Abstract It is believed that the large-scale geometric properties of two-dimensional critical percolation are described by a logarithmic conformal field theory, but it has been challenging to exhibit concrete examples of logarithmic singularities and to find an explanation and a physical interpretat...
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SpringerOpen
2024-08-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP08(2024)103 |
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| author | Federico Camia Yu Feng |
| author_facet | Federico Camia Yu Feng |
| author_sort | Federico Camia |
| collection | DOAJ |
| description | Abstract It is believed that the large-scale geometric properties of two-dimensional critical percolation are described by a logarithmic conformal field theory, but it has been challenging to exhibit concrete examples of logarithmic singularities and to find an explanation and a physical interpretation, in terms of lattice observables, for their appearance. We show that certain percolation correlation functions receive independent contributions from a large number of similar connectivity events happening at different scales. Combined with scale invariance, this leads to logarithmic divergences. We study several logarithmic correlation functions for critical percolation in the bulk and in the presence of a boundary, including the four-point function of the density (spin) field. Our analysis confirms previous findings, provides new explicit calculations and explains, in terms of lattice observables, the physical mechanism that leads to the logarithmic singularities we discover. Although we adopt conformal field theory (CFT) terminology to present our results, the core of our analysis relies on probabilistic arguments and recent rigorous results on the scaling limit of critical percolation and does not assume a priori the existence of a percolation CFT. As a consequence, our results provide strong support for the validity of a CFT description of critical percolation and a step in the direction of a mathematically rigorous formulation of a logarithmic CFT of two-dimensional critical percolation. |
| format | Article |
| id | doaj-art-cb852ebfdce146f991ac70b0e19e3d0f |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-cb852ebfdce146f991ac70b0e19e3d0f2024-11-24T12:05:27ZengSpringerOpenJournal of High Energy Physics1029-84792024-08-012024812510.1007/JHEP08(2024)103Logarithmic correlation functions in 2D critical percolationFederico Camia0Yu Feng1Science Division, New York University Abu DhabiDepartment of Mathematics, Tsinghua UniversityAbstract It is believed that the large-scale geometric properties of two-dimensional critical percolation are described by a logarithmic conformal field theory, but it has been challenging to exhibit concrete examples of logarithmic singularities and to find an explanation and a physical interpretation, in terms of lattice observables, for their appearance. We show that certain percolation correlation functions receive independent contributions from a large number of similar connectivity events happening at different scales. Combined with scale invariance, this leads to logarithmic divergences. We study several logarithmic correlation functions for critical percolation in the bulk and in the presence of a boundary, including the four-point function of the density (spin) field. Our analysis confirms previous findings, provides new explicit calculations and explains, in terms of lattice observables, the physical mechanism that leads to the logarithmic singularities we discover. Although we adopt conformal field theory (CFT) terminology to present our results, the core of our analysis relies on probabilistic arguments and recent rigorous results on the scaling limit of critical percolation and does not assume a priori the existence of a percolation CFT. As a consequence, our results provide strong support for the validity of a CFT description of critical percolation and a step in the direction of a mathematically rigorous formulation of a logarithmic CFT of two-dimensional critical percolation.https://doi.org/10.1007/JHEP08(2024)103Lattice Quantum Field TheoryRandom SystemsScale and Conformal SymmetriesStochastic Processes |
| spellingShingle | Federico Camia Yu Feng Logarithmic correlation functions in 2D critical percolation Journal of High Energy Physics Lattice Quantum Field Theory Random Systems Scale and Conformal Symmetries Stochastic Processes |
| title | Logarithmic correlation functions in 2D critical percolation |
| title_full | Logarithmic correlation functions in 2D critical percolation |
| title_fullStr | Logarithmic correlation functions in 2D critical percolation |
| title_full_unstemmed | Logarithmic correlation functions in 2D critical percolation |
| title_short | Logarithmic correlation functions in 2D critical percolation |
| title_sort | logarithmic correlation functions in 2d critical percolation |
| topic | Lattice Quantum Field Theory Random Systems Scale and Conformal Symmetries Stochastic Processes |
| url | https://doi.org/10.1007/JHEP08(2024)103 |
| work_keys_str_mv | AT federicocamia logarithmiccorrelationfunctionsin2dcriticalpercolation AT yufeng logarithmiccorrelationfunctionsin2dcriticalpercolation |