Uniform analyticity of local observables in FK-percolation and analyticity of the Ising spontaneous magnetisation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910149338202112 |
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| author | D'Alimonte, Lucas Gassmann, Loïc |
| author_facet | D'Alimonte, Lucas Gassmann, Loïc |
| contents | We prove that, in the FK-percolation model, the probabilities of local events are uniformly analytic in the percolation parameter $p$ under suitable mixing assumptions on the measure, and satisfy a uniform exponential growth bound. This result allows us to prove that the magnetisation of the Potts model is analytic in a suitable range of parameters, including the Ising case in all dimensions $d \geq 3$ in the whole supercritical regime. We also provide a proof of the analyticity of the susceptibility of the Potts model with $q$ colours, for any $q \geq 2$ in the whole subcritical interval. Finally, we prove the analyticity of various quantities in the FK-percolation measure, including the multi-point and truncated multi-point connectivity probabilities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18558 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uniform analyticity of local observables in FK-percolation and analyticity of the Ising spontaneous magnetisation D'Alimonte, Lucas Gassmann, Loïc Probability Mathematical Physics 60K35, 82B20, 82B43 We prove that, in the FK-percolation model, the probabilities of local events are uniformly analytic in the percolation parameter $p$ under suitable mixing assumptions on the measure, and satisfy a uniform exponential growth bound. This result allows us to prove that the magnetisation of the Potts model is analytic in a suitable range of parameters, including the Ising case in all dimensions $d \geq 3$ in the whole supercritical regime. We also provide a proof of the analyticity of the susceptibility of the Potts model with $q$ colours, for any $q \geq 2$ in the whole subcritical interval. Finally, we prove the analyticity of various quantities in the FK-percolation measure, including the multi-point and truncated multi-point connectivity probabilities. |
| title | Uniform analyticity of local observables in FK-percolation and analyticity of the Ising spontaneous magnetisation |
| topic | Probability Mathematical Physics 60K35, 82B20, 82B43 |
| url | https://arxiv.org/abs/2604.18558 |