On the duality between height functions and continuous spin models
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908592297213952 |
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| author | van Engelenburg, Diederik Lis, Marcin |
| author_facet | van Engelenburg, Diederik Lis, Marcin |
| contents | We revisit the classical phenomenon of duality between random integer-valued height functions with positive definite potentials and abelian spin models with O(2) symmetry. We use it to derive new results in quite high generality including: a universal upper bound on the variance of the height function in terms of the Green's function (a GFF bound) which among others implies localisation on transient graphs; monotonicity of said variance with respect to a natural temperature parameter; the fact that delocalisation of the height function implies a BKT phase transition in planar models; and also delocalisation itself for height functions on periodic ``almost'' planar graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_08596 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the duality between height functions and continuous spin models van Engelenburg, Diederik Lis, Marcin Probability Mathematical Physics We revisit the classical phenomenon of duality between random integer-valued height functions with positive definite potentials and abelian spin models with O(2) symmetry. We use it to derive new results in quite high generality including: a universal upper bound on the variance of the height function in terms of the Green's function (a GFF bound) which among others implies localisation on transient graphs; monotonicity of said variance with respect to a natural temperature parameter; the fact that delocalisation of the height function implies a BKT phase transition in planar models; and also delocalisation itself for height functions on periodic ``almost'' planar graphs. |
| title | On the duality between height functions and continuous spin models |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2303.08596 |