Ising model close to $d=2$

Wenliang Li

doi:10.1103/physrevd.105.l091902

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arXiv · 2107.13679

Ising model close to $d=2$

Wenliang Li

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Abstract

The $d=2$ critical Ising model is described by an exactly solvable Conformal Field Theory (CFT). The deformation to $d=2+\epsilon$ is a relatively simple system at strong coupling outside of even dimensions. Using novel numerical and analytical conformal bootstrap methods in Lorentzian signature, we show that the leading corrections to the Ising data are more singular than $\epsilon$. There must be infinitely many new states due to the $d$-dependence of conformal symmetry. The linear independence of conformal blocks is central to this bootstrap approach, which can be extended to more rigorous studies of non-positive systems, such as non-unitary, defect/boundary and thermal CFTs.

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Wenliang Li. 2021-07-29. Ising model close to $d=2$. https://doi.org/10.1103/physrevd.105.l091902

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