Universality in the 2d quasi-periodic Ising model and Harris-Luck irrelevance

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.

arXiv comment40 pages, 6 figures. Version accepted for publication in Comm. Math. Phys

References in corpus (30)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Twistless KAM tori
• Localization Bounds for an Electron Gas
• Localization of interacting fermions in the Aubry-Andre' model
• Introduction to a renormalisation group method
• Rounding of First Order Transitions in Low-Dimensional Quantum Systems with Quenched Disorder
• Anomalous universality in the anisotropic Ashkin-Teller model
• The Ising Susceptibility Scaling Function
• The quasi-periodic quantum Ising transition in 1D
• Anderson localization for multi-frequency quasi-periodic operators on ${\mathbb{Z}}^d$
• The scaling limit of the energy correlations in non integrable Ising models
• Universal Relations for Non Solvable Statistical Models
• Extended scaling relations for planar lattice models
• Localization in interacting fermionic chains with quasi-random disorder
• Non-integrable dimers: Universal fluctuations of tilted height profiles
• Emergent Planarity in two-dimensional Ising Models with finite-range Interactions
• Small denominators and anomalous behaviour in the Holstein-Hubbard model
• A power-law upper bound on the correlations in the 2D random field Ising model
• Energy correlations of non-integrable Ising models: The scaling limit in the cylinder
• Universal finite size corrections and the central charge in non solvable Ising models
• Stability of Weyl semimetals with quasiperiodic disorder
• Localization in an interacting quasi-periodic fermionic chain
• Dense gaps and scaling relations in the interacting Aubry-Andre' model
• Lyapunov exponent for products of random Ising transfer matrices: the balanced disorder case
• Persistence of gaps in the interacting Hofstadter model
• Coupled identical localized fermionic chains with quasi-random disorder
• Discrete and zeta-regularized determinants of the Laplacian on polygonal domains with Dirichlet boundary conditions
• The Site-Diluted Ising Model in Four Dimension
• Interacting spinning fermions with quasi-random disorder
• Vanishing of Drude weight in interacting fermions on Zd with quasi-periodic disorder

Cited by in corpus (2)

• Fragile magnetic order in metallic quasicrystals
• The scaling limit of boundary spin correlations in non-integrable Ising models