User:Sylvain Ribault/Bootstat2021/Cappelli

Bootstrapping the Ising model between 2 and 4 dimensions using the conformal bootstrap.

Ising model is a singular point of the boundary of the allowed region in the unitary bootstrap. So it obeys a sort of reduced bootstrap. It is a kind of minimal model. Unitary line corresponds to the relation

(d=2) \qquad \Delta_{(1,3)}(c) = \frac83 \Delta_{(1,2)}(c) + \frac23 $$ Approximate similar relation for $$2\leq d\leq 3$$.

Let us consider 13 values of the dimension in that interval. We restrict to the six lowest states, checked against the best $$d=3$$ results. Then polynomial fit in $$y=4-d$$. Get conformal dimensions with about 4 significant digits.

Comparison with other results for conformal dimensions: Monte-Carlo, resummed $$\epsilon$$ expansion.