Universality in the 2d quasi-periodic Ising model and Harris-Luck irrelevance
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2023
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| _version_ | 1866910675490570240 |
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| author | Gallone, Matteo Mastropietro, Vieri |
| author_facet | Gallone, Matteo Mastropietro, Vieri |
| contents | We prove that in the 2d Ising Model with a weak bidimensional quasi-periodic disorder in the interaction, the critical behavior is the same as in the non-disordered case, that is the critical exponents for the specific heat and energy-energy correlations are identical and no logarithmic corrections are present. The disorder produces a quasi-periodic modulation of the amplitude of the correlations and a renormalization of the velocities, that is the coefficients of the rescaling of positions, and of the critical temperature. The result establishes the validity of the prediction based on the Harris-Luck criterion and it provides the first rigorous proof of universality in the Ising model in presence of quasi-periodic disorder in both directions and for any angle. Small divisors are controlled assuming a Diophantine condition on the frequencies and convergence of the series is proved by Renormalization Group analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01736 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Universality in the 2d quasi-periodic Ising model and Harris-Luck irrelevance Gallone, Matteo Mastropietro, Vieri Mathematical Physics Statistical Mechanics We prove that in the 2d Ising Model with a weak bidimensional quasi-periodic disorder in the interaction, the critical behavior is the same as in the non-disordered case, that is the critical exponents for the specific heat and energy-energy correlations are identical and no logarithmic corrections are present. The disorder produces a quasi-periodic modulation of the amplitude of the correlations and a renormalization of the velocities, that is the coefficients of the rescaling of positions, and of the critical temperature. The result establishes the validity of the prediction based on the Harris-Luck criterion and it provides the first rigorous proof of universality in the Ising model in presence of quasi-periodic disorder in both directions and for any angle. Small divisors are controlled assuming a Diophantine condition on the frequencies and convergence of the series is proved by Renormalization Group analysis. |
| title | Universality in the 2d quasi-periodic Ising model and Harris-Luck irrelevance |
| topic | Mathematical Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2304.01736 |