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Mathematical Physics
Title: Universality in the 2d quasi-periodic Ising model and Harris-Luck irrelevance
(Submitted on 4 Apr 2023 (v1), last revised 7 Apr 2024 (this version, v3))
Abstract: 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.
Submission history
From: Matteo Gallone [view email][v1] Tue, 4 Apr 2023 12:09:27 GMT (38kb)
[v2] Tue, 21 Nov 2023 10:50:56 GMT (52kb)
[v3] Sun, 7 Apr 2024 10:43:25 GMT (68kb)
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