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3D Ising CFT and Exact Diagonalization on Icosahedron: The Power of Conformal Perturbation Theory (2307.02540v4)

Published 5 Jul 2023 in hep-th, cond-mat.stat-mech, and cond-mat.str-el

Abstract: 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 $\mathbb{R}\times S2$, 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 $S2$. Its ideal arena of application should be the recently proposed models of fuzzy sphere regularization.

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