二维准周期 Ising 模型中的普适性与 Harris–Luck 无关性
Universality in the 2d quasi-periodic Ising model and Harris-Luck irrelevance
AI总结：
本文用重整化群证明二维双向准周期弱无序 Ising 模型仍保持纯模型临界指数且无对数修正，严格验证 Harris–Luck 无关性预测。
摘要：
我们证明，在相互作用中具有弱二维准周期无序的二维 Ising 模型中，其临界行为与无序情形相同：也就是说，比热和能量—能量关联函数的临界指数完全一致，并且不存在对数修正。无序会使关联函数的振幅产生准周期调制，并导致速度（即位置重标度的系数）以及临界温度发生重整化。该结果确立了基于 Harris–Luck 判据所作预测的有效性，并首次严格证明了在两个方向上均存在准周期无序且适用于任意角度的 Ising 模型中的普适性。小除数问题通过对频率施加 Diophantine 条件加以控制，而级数的收敛性则通过重整化群分析得到证明。
英文摘要：
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.
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