  We present precise multilevel exponential concentration inequalities for
polynomials in Ising models satisfying the Dobrushin condition. The estimates
have the same form as two-sided tail estimates for polynomials in Gaussian
variables due to Lata{\l}a. In particular, for quadratic forms we obtain a
Hanson-Wright type inequality.
  We also prove concentration results for convex functions and estimates for
nonnegative definite quadratic forms, analogous as for quadratic forms in
i.i.d. Rademacher variables, for more general random vectors satisfying the
approximate tensorization property for entropy.
