2.01维和3维无规键伊辛模型
The Random-Bond Ising Model in 2.01 and 3 Dimensions
摘要：
我们考虑了二维和四维之间的伊辛模型，它受到附近自旋之间相互作用强度的淬火无序的扰动。在2<d<4的区间内，这种无序是一种相关的扰动，它将系统驱动到重整化群的一个新的不动点。在d=2时，这样的无序是不相关的，可以用共形微扰理论来研究。结合共形扰动理论与最近的结果，从共形引导，我们计算一些标度指数在d=2左右的扩展。如果在d=3的情况下也相信这些计算，则发现结果与实验数据和蒙特卡罗模拟一致。此外，我们进行了直接的不受控制的计算，在d=3使用新的结果，在3d伊辛模型的低洼运营商的尺寸和OPE系数。我们将这些新方法与以前的研究进行了比较。最后，我们评论的$O(2)$模型在d=3，在那里我们预测一个大的对数校正的红外标度的障碍。
英文摘要：
We consider the Ising model between 2 and 4 dimensions perturbed by quenched disorder in the strength of the interaction between nearby spins. In the interval 2<d<4 this disorder is a relevant perturbation that drives the system to a new fixed point of the renormalization group. At d=2 such disorder is marginally irrelevant and can be studied using conformal perturbation theory. Combining conformal perturbation theory with recent results from the conformal bootstrap we compute some scaling exponents in an expansion around d=2. If one trusts these computations also in d=3, one finds results consistent with experimental data and Monte Carlo simulations. In addition, we perform a direct uncontrolled computation in d=3 using new results for low-lying operator dimensions and OPE coefficients in the 3d Ising model. We compare these new methods with previous studies. Finally, we comment about the $O(2)$ model in d=3, where we predict a large logarithmic correction to the infrared scaling of disorder.
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