3D Ising CFT与二十面体上的精确对角化：共形微扰论的威力
3D Ising CFT and Exact Diagonalization on Icosahedron: The Power of Conformal Perturbation Theory
AI总结：
本研究将12个自旋置于正二十面体顶点构建(2+1)维横场Ising模型，通过引入含少数局域算符的CFT哈密顿量有效微扰，验证了其可与3D Ising CFT对比，展现了共形微扰论在模糊球正则化等场景的应用潜力。
摘要：
我们研究(2+1)维横场Ising模型，将12个自旋置于正二十面体的顶点。按精确对角化的标准来看该模型规模极小，且破坏旋转不变性。但我们证明，通过引入含少数局域算符的CFT哈密顿量有效微扰，它能与$\u211d\times S^2$上的3D Ising CFT进行有意义的比较。这个极端例子展现了共形微扰论在理解正则化$S^2$上模型的有限$N$效应方面的威力，其理想应用场景应为近期提出的模糊球正则化模型。
英文摘要：
We consider the transverse field Ising model in $(2+1)$D, putting 12 spins at the vertices of the regular icosahedron. The model is tiny by the exact diagonalization standards, and breaks rotation invariance. Yet we show that it allows a meaningful comparison to the 3D Ising CFT on $\mathbb{R}\times S^2$, by including effective perturbations of the CFT Hamiltonian with a handful of local operators. This extreme example shows the power of conformal perturbation theory in understanding finite $N$ effects in models on regularized $S^2$. Its ideal arena of application should be the recently proposed models of fuzzy sphere regularization.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
