The presence of dangerously irrelevant operators leads to the violation of the hyperscaling relation α α = 2 − − d ν ν between the critical exponents α α and ν ν in d dimensions. The simplest example ( p. 93) is the critical point of the Ising ferromagnet in d ≥ ≥ 4 dimensions, which is a gaussian theory (free massless scalar ϕ ϕ ), but the leading irrelevant perturbation ϕ ϕ 4 is dangerously irrelevant. Another example occurs for the Ising model with random-field disorder, where the fixed point occurs at zero temperature, and the temperature perturbation is dangerously irrelevant ( p. 164).