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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">najo</journal-id><journal-title-group><journal-title xml:lang="en">Nanosystems: Physics, Chemistry, Mathematics</journal-title><trans-title-group xml:lang="ru"><trans-title>Наносистемы: физика, химия, математика</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2220-8054</issn><issn pub-type="epub">2305-7971</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17586/2220-8054-2015-6-2-274-279</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-932</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>REGULAR PAPERS</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>REGULAR PAPERS</subject></subj-group></article-categories><title-group><article-title>Renyi entropy for the doped graphene at low temperatures</article-title><trans-title-group xml:lang="ru"><trans-title></trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Konobeeva</surname><given-names>N. N.</given-names></name></name-alternatives><bio xml:lang="en"><p>Volgograd</p></bio><email xlink:type="simple">yana_nn@inbox.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Polunina</surname><given-names>A. A.</given-names></name></name-alternatives><bio xml:lang="en"><p>Volgograd</p></bio><email xlink:type="simple">polunina_a@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Belonenko</surname><given-names>M. B.</given-names></name></name-alternatives><bio xml:lang="en"><p>Volgograd</p></bio><email xlink:type="simple">mbelonenko@yandex.ru</email><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff xml:lang="en" id="aff-1"><institution>Volgograd State University</institution><country>Russian Federation</country></aff><aff xml:lang="en" id="aff-2"><institution>Volgograd State University; Volgograd Institute of Business</institution><country>Russian Federation</country></aff><pub-date pub-type="collection"><year>2015</year></pub-date><pub-date pub-type="epub"><day>14</day><month>08</month><year>2025</year></pub-date><volume>6</volume><issue>2</issue><fpage>274</fpage><lpage>279</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Konobeeva N.N., Polunina A.A., Belonenko M.B., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Konobeeva N.N., Polunina A.A., Belonenko M.B.</copyright-holder><copyright-holder xml:lang="en">Konobeeva N.N., Polunina A.A., Belonenko M.B.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://nanojournal.ifmo.ru/jour/article/view/932">https://nanojournal.ifmo.ru/jour/article/view/932</self-uri><abstract><p>The distribution function for the perimeter of a simply connected cluster containing undoped lattice sites is based on percolation theory and the hypothesis of scale invariance. The Renyi entropy for doped graphene at low temperatures was calculated on the basis of this distribution function.</p></abstract><kwd-group xml:lang="en"><kwd>nanostructure</kwd><kwd>graphene</kwd><kwd>Renyi entropy</kwd></kwd-group><funding-group><funding-statement xml:lang="en">This work was supported by the Russian Foundation for Basic Research under project No. 12-02-31654.</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Kirchanov V.S. Using the Renyi entropy to describe quantum dissipative systems in statistical mechanics. Theoretical and Mathematical Physics, 156(3), P. 444–453 (2008).</mixed-citation><mixed-citation xml:lang="en">Kirchanov V.S. Using the Renyi entropy to describe quantum dissipative systems in statistical mechanics. Theoretical and Mathematical Physics, 156(3), P. 444–453 (2008).</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Chumak O.V. Entropy and fractals in data analysis. Moscow, Izhevsk: SRC “Regular and Chaotic Dynamics”, Institute of Computer Science, 164 p. (2011).</mixed-citation><mixed-citation xml:lang="en">Chumak O.V. Entropy and fractals in data analysis. Moscow, Izhevsk: SRC “Regular and Chaotic Dynamics”, Institute of Computer Science, 164 p. (2011).</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Hawking S.W. Black hole and thermodynamics collection of articles “Black hole”. News of fundamental physics. Issue 9. P. 204–221 (1978).</mixed-citation><mixed-citation xml:lang="en">Hawking S.W. Black hole and thermodynamics collection of articles “Black hole”. News of fundamental physics. Issue 9. P. 204–221 (1978).</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Schroeder M. Fractals, Chaos, Power Laws. Moscow, Izhevsk: R&amp;C Dynamics, 527 p. (2001).</mixed-citation><mixed-citation xml:lang="en">Schroeder M. Fractals, Chaos, Power Laws. Moscow, Izhevsk: R&amp;C Dynamics, 527 p. (2001).</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Assaad F.F., Lang T.C., Parisen Toldin F. Entanglement Spectra of Interacting Fermions in Quantum Monte Carlo Simulations (2013). (http://arxiv.org/pdf/1311.5851.pdf).</mixed-citation><mixed-citation xml:lang="en">Assaad F.F., Lang T.C., Parisen Toldin F. Entanglement Spectra of Interacting Fermions in Quantum Monte Carlo Simulations (2013). (http://arxiv.org/pdf/1311.5851.pdf).</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Xiong H., Wu B. Atomic Quantum Corrals for Bose-Einstein Condensates. Phys. Rev. A., 82, P. 053634 (2010).</mixed-citation><mixed-citation xml:lang="en">Xiong H., Wu B. Atomic Quantum Corrals for Bose-Einstein Condensates. Phys. Rev. A., 82, P. 053634 (2010).</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Rossi E., Morr D.K. Spatially dependent Kondo effect in Quantum Corrals. Phys. Rev. Lett., 97, P. 236602 (2006).</mixed-citation><mixed-citation xml:lang="en">Rossi E., Morr D.K. Spatially dependent Kondo effect in Quantum Corrals. Phys. Rev. Lett., 97, P. 236602 (2006).</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Novoselov K.S., Geim A.K., Morozov S.V., Jiang D., Katsnelson M.I., Grigorieva I.V., Firsov A.A. Two-dimensional gas of massless Dirac fermions in graphene. Nature, 438, P. 197 (2005).</mixed-citation><mixed-citation xml:lang="en">Novoselov K.S., Geim A.K., Morozov S.V., Jiang D., Katsnelson M.I., Grigorieva I.V., Firsov A.A. Two-dimensional gas of massless Dirac fermions in graphene. Nature, 438, P. 197 (2005).</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Datta S., David J.R. Renyi entropies of free bosons on the torus and holography (2013). (http://arxiv.org/pdf/1311.1218.pdf).</mixed-citation><mixed-citation xml:lang="en">Datta S., David J.R. Renyi entropies of free bosons on the torus and holography (2013). (http://arxiv.org/pdf/1311.1218.pdf).</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Patashinskii A.Z., Pokrovskii V.L. Fluctuation theory of phase transitions. Moscow: Nauka, 381 p. (1982).</mixed-citation><mixed-citation xml:lang="en">Patashinskii A.Z., Pokrovskii V.L. Fluctuation theory of phase transitions. Moscow: Nauka, 381 p. (1982).</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">M¨uller H. Scaling as a fundamental property of natural vibrations of matter and the fractal structure of space-time. Foundations of physics and geometry. P. 189–209 (2008).</mixed-citation><mixed-citation xml:lang="en">M¨uller H. Scaling as a fundamental property of natural vibrations of matter and the fractal structure of space-time. Foundations of physics and geometry. P. 189–209 (2008).</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Gusynin V. P., Shaparov S.G., Carbotte J.P. AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics. Int. J. Mod. Phys. B., 21, P. 4611–4658 (2007).</mixed-citation><mixed-citation xml:lang="en">Gusynin V. P., Shaparov S.G., Carbotte J.P. AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics. Int. J. Mod. Phys. B., 21, P. 4611–4658 (2007).</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Castro Neto A.H., Guinea F., Peres N.M.R., Novoselov K.S., Geim A.K. The electronic properties of graphene. Rev. Mod. Phys., 81, P. 109 (2009).</mixed-citation><mixed-citation xml:lang="en">Castro Neto A.H., Guinea F., Peres N.M.R., Novoselov K.S., Geim A.K. The electronic properties of graphene. Rev. Mod. Phys., 81, P. 109 (2009).</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Logemann R., Reijnders K.J.A., Tudorovskiy T., Katsnelson M.I., Yuan S. Modeling Klein Tunneling and Caustics of Electron Waves in Graphene (2014). (http://arxiv.org/pdf/1409.1277v1.pdf).</mixed-citation><mixed-citation xml:lang="en">Logemann R., Reijnders K.J.A., Tudorovskiy T., Katsnelson M.I., Yuan S. Modeling Klein Tunneling and Caustics of Electron Waves in Graphene (2014). (http://arxiv.org/pdf/1409.1277v1.pdf).</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Gantmaher V.F. Electrons in disordered media. Moscow: Fizmatlit, 288 p. (2013).</mixed-citation><mixed-citation xml:lang="en">Gantmaher V.F. Electrons in disordered media. Moscow: Fizmatlit, 288 p. (2013).</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
