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Description
The Ising model in $d>2$ is characterized by the OPEs $\sigma \times \sigma = 1 + \epsilon + \cdots$ and $\epsilon \times \epsilon = 1 + \epsilon + \cdots$. In $d=2$, the OPE coefficient $C_{\epsilon\epsilon\epsilon}= 0$, and this is explained by duality, leading to solvability and the absence of fine-tuning. We explore the possibility of demanding $C_{\epsilon\epsilon\epsilon} = 0$ in higher dimensions using the conformal bootstrap. Such a theory, if any, will solve the fine-tuning problem, offering a new mechanism for self-organized criticality. We show that in $d=2$ with this ansatz, the Ising model can be isolated to the tip of a very thin nose, and you will see what happens in $d>2$. During the search, you will also encounter an enigmatic, potentially spurious feature from the phenomenon called "trivial mix problem" by Ning Su.