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arXiv · 2511.15160

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

D. Shapoval·M. Dudka
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Abstract

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

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D. Shapoval, M. Dudka. 2025-11-19. Critical exponents of the Ising model with quenched structural disorder and long-range interactions at spatial dimension $d=3$. https://doi.org/10.5488/cmp.28.43503

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