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arXiv:2610.25940

The long-range Ising CFT: perturbative and nonperturbative approaches

郑则川

Published Oct 19, 2026• 0 citations
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Abstract

The long-range Ising model is the prototype of criticality with power-law interactions. In each dimension its interacting critical points form a one-parameter family of nonlocal conformal field theories, weakly coupled at both ends but not in between. We study this family in one, two and three dimensions from several independent directions. We extend the expansion about the generalized free field from three to eight loops and expand about the short-range end. We show that Hamiltonian truncation applies to this nonlocal theory once a truncation artifact is corrected. Where they can be compared, the resummed expansions, Hamiltonian truncation, the numerical renormalization group and Monte Carlo simulations agree on the dimension of the leading $\mathbb{Z}_2$-even scalar at the sub-percent level, as universality requires.

DOI
10.48550/arxiv.2610.25940

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