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

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Title: Critical exponents of the Ising model with quenched structural disorder and long-range interactions at spatial dimension 𝒅 = 3.
Alternate Title: Критичнi показники моделi Iзiнга iз замороженим структурним безладом та далекосяжними взаємодiями при вимiрностi простору 𝒅 = 3
Authors: Shapoval, D.1,2 shapoval@icmp.lviv.ua, Dudka, M.1,2,3
Source: Condensed Matter Physics. 2025, Vol. 28 Issue 4, p1-14. 14p.
Subjects: Critical exponents, Ising model, Renormalization group, Mathematics
Abstract: We analyse the critical properties of a weakly diluted (random) Ising model with the long-range interaction decaying with distance 𝑥 as ∼ 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. [ABSTRACT FROM AUTHOR]
Copyright of Condensed Matter Physics is the property of National Academy of Sciences of Ukraine, the Institute for Condensed Matter Physics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Critical exponents of the Ising model with quenched structural disorder and long-range interactions at spatial dimension 𝒅 = 3.
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  Data: Критичнi показники моделi Iзiнга iз замороженим структурним безладом та далекосяжними взаємодiями при вимiрностi простору 𝒅 = 3
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  Data: <searchLink fieldCode="AR" term="%22Shapoval%2C+D%2E%22">Shapoval, D.</searchLink><relatesTo>1,2</relatesTo><i> shapoval@icmp.lviv.ua</i><br /><searchLink fieldCode="AR" term="%22Dudka%2C+M%2E%22">Dudka, M.</searchLink><relatesTo>1,2,3</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22Condensed+Matter+Physics%22">Condensed Matter Physics</searchLink>. 2025, Vol. 28 Issue 4, p1-14. 14p.
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  Data: <searchLink fieldCode="DE" term="%22Critical+exponents%22">Critical exponents</searchLink><br /><searchLink fieldCode="DE" term="%22Ising+model%22">Ising model</searchLink><br /><searchLink fieldCode="DE" term="%22Renormalization+group%22">Renormalization group</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink>
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  Data: We analyse the critical properties of a weakly diluted (random) Ising model with the long-range interaction decaying with distance 𝑥 as ∼ 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. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Group: Ab
  Data: <i>Copyright of Condensed Matter Physics is the property of National Academy of Sciences of Ukraine, the Institute for Condensed Matter Physics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.5488/CMP.28.43503
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        Text: English
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              Text: 2025
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