Critical exponents of the Ising model with quenched structural disorder and long-range interactions at spatial dimension $d=3$
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| Format: | Preprint |
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2025
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| _version_ | 1866918264957829120 |
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| author | Shapoval, D. Dudka, M. |
| author_facet | Shapoval, D. Dudka, M. |
| contents | 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 renormalization 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_15160 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Critical exponents of the Ising model with quenched structural disorder and long-range interactions at spatial dimension $d=3$ Shapoval, D. Dudka, M. Statistical Mechanics 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 renormalization 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. |
| title | Critical exponents of the Ising model with quenched structural disorder and long-range interactions at spatial dimension $d=3$ |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2511.15160 |