Critical exponents of the Ising model with quenched structural disorder and long-range interactions at spatial dimension $d=3$

Abstract: We analyse the critical properties of a weakly diluted (random) Ising model with the long-range interaction decaying with distance $x$ as $\sim x^{-d-σ}$ in a $d$-dimensional space. It is known to belong to a new long-range random universality class for certain values of the decay parameter $σ$. Exploiting the field-theoretic renormalization group approach within the minimal subtraction scheme, we compute the three-loop rermalization group functions. On their basis, with the help of asymptotic series resummation methods, we estimate the correlation length critical exponent $ν$ characterising the new universality class for $d=3$ and for those values of $σ$ for which long-range interactions are relevant for the critical behaviour.