Exact critical exponents for vector operators in the 3d Ising model and conformal invariance

Gonzalo De Polsi; Matthieu Tissier; Nicolás Wschebor

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arXiv · 1804.08374

Exact critical exponents for vector operators in the 3d Ising model and conformal invariance

Gonzalo De Polsi·Matthieu Tissier·Nicolás Wschebor

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Abstract

It is widely expected that the realization of scale invariance in the critical regime implies conformal invariance for a large class of systems. This is known to be true if there exist no integrated operator which transforms like a vector under rotations and which has scaling dimension $-1$. In this article we give exact expressions for the critical exponents of some of these vector operators. In particular, we show that one operator has scaling dimension exactly 3 in any space dimension. This operator turns out be the leading operator at least in $d=2$ and $d=4$. Moreover, we prove that the operator previously considered in Monte-Carlo simulations has also scaling dimension exactly $3$ in any dimension.

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Gonzalo De Polsi, Matthieu Tissier, Nicolás Wschebor. 2018-04-23. Exact critical exponents for vector operators in the 3d Ising model and conformal invariance. https://arxiv.org/abs/1804.08374

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