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<p>This work analyzes the magnetic properties of a ferromagnetic B<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6136_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(_{36}\)</EquationSource> </InlineEquation> borophene-like monolayer, described by the spin-3/2 Blume-Capel model in the presence of a two-dimensional crystal field. The method is based on the mean-field approximation using the Gibbs-Bogoliubov inequality. We study the effect of temperature (<i>T</i>) and both longitudinal (<i>D</i>) and transverse (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6136_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Gamma\)</EquationSource> </InlineEquation>) crystal fields on the magnetization and the phase diagrams in the (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6136_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Gamma\)</EquationSource> </InlineEquation>, <i>T</i>) and (<i>D</i>, <i>T</i>) planes. The results reveal first- and second-order phase transitions, along with critical, bicritical, and multicritical points, as well as highly degenerate states at <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6136_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\(T = 0\)</EquationSource> </InlineEquation>.</p>

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Phase Diagrams of a Blume-Capel B36 Borophene-Like Monolayer in a Transverse Crystal Field

  • 期刊论文

  • 发表日期：

    2025年10月6日

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  • A. El Abbassi,
  • M. Salama,
  • N. Hachem,
  • E. B. Choubabi,
  • M. El Bouziani

摘要

This work analyzes the magnetic properties of a ferromagnetic B \(_{36}\) borophene-like monolayer, described by the spin-3/2 Blume-Capel model in the presence of a two-dimensional crystal field. The method is based on the mean-field approximation using the Gibbs-Bogoliubov inequality. We study the effect of temperature (T) and both longitudinal (D) and transverse ( \(\Gamma\) ) crystal fields on the magnetization and the phase diagrams in the ( \(\Gamma\) , T) and (D, T) planes. The results reveal first- and second-order phase transitions, along with critical, bicritical, and multicritical points, as well as highly degenerate states at \(T = 0\) .