Near-critical Ising, sine-Gordon at the free fermion point, and bosonization
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arXiv
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| Format: | Preprint |
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2025
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| author | Park, S. C. Virtanen, Tuomas Webb, Christian |
| author_facet | Park, S. C. Virtanen, Tuomas Webb, Christian |
| contents | In this article, we study the continuous correlations of the near-critical Ising model in two dimensions with plus boundary conditions, and prove that doubled correlation functions of primary fields (spin, disorder, fermions, energy) in the Ising model are given by correlation functions of the sine-Gordon model at the free fermion point. This is an instance of bosonization.
The main ideas involve analyticity of correlation functions in a mass parameter in finite volume and proving that in a perturbative regime, the Taylor coefficients of the correlation functions match due to known bosonization results for the critical Ising model in terms of the Gaussian free field.
The main techniques on the Ising side involve construction and precise estimates of certain massive holomorphic functions while on the sine-Gordon side, we control an iterated Mayer expansion with techniques going back to Brydges and Kennedy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11304 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Near-critical Ising, sine-Gordon at the free fermion point, and bosonization Park, S. C. Virtanen, Tuomas Webb, Christian Mathematical Physics Probability In this article, we study the continuous correlations of the near-critical Ising model in two dimensions with plus boundary conditions, and prove that doubled correlation functions of primary fields (spin, disorder, fermions, energy) in the Ising model are given by correlation functions of the sine-Gordon model at the free fermion point. This is an instance of bosonization. The main ideas involve analyticity of correlation functions in a mass parameter in finite volume and proving that in a perturbative regime, the Taylor coefficients of the correlation functions match due to known bosonization results for the critical Ising model in terms of the Gaussian free field. The main techniques on the Ising side involve construction and precise estimates of certain massive holomorphic functions while on the sine-Gordon side, we control an iterated Mayer expansion with techniques going back to Brydges and Kennedy. |
| title | Near-critical Ising, sine-Gordon at the free fermion point, and bosonization |
| topic | Mathematical Physics Probability |
| url | https://arxiv.org/abs/2512.11304 |