On the new universality class in structurally disordered $n$-vector model with long-range interactions

Abstract

We study a stability border of a region where nontrivial critical behaviour of an $n$-vector model with long-range power-law decaying interactions is induced by the presence of a structural disorder (e.g. weak quenched dilution). This border is given by the marginal dimension of the order parameter $n_c$ dependent on space dimension, $d$, and a control parameter of the interaction decay, $\sigma$, below which the model belongs to the new dilution-induced universality class. Exploiting the Harris criterion and recent field-theoretical renormalization group results for the pure model with long-range interactions we get $n_c$ as a three loop $\epsilon =2\sigma -d$-expansion. We provide numerical values for $n_c$ applying series resummation methods. Our results show that not only the Ising systems ($n=1$) can belong to the new disorder-induced long-range universality class at $d=2$ and $d=3$.

arXiv comment13 pages, 1 figure, submitted to the Festschrift on the occasion of A. S. Davydov's 110th anniversary

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Cited by in corpus (1)

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