The Random-Bond Ising Model in 2.01 and 3 Dimensions

Understand

We consider the Ising model between 2 and 4 dimensions perturbed by quenched disorder in the strength of the interaction between nearby spins.

• In the interval 2<d<4 this disorder is a relevant perturbation that drives the system to a new fixed point of the renormalization group.
• At d=2 such disorder is marginally irrelevant and can be studied using conformal perturbation theory.
• Combining conformal perturbation theory with recent results from the conformal bootstrap we compute some scaling exponents in an expansion around d=2.