Free Energy of Three-Dimensional Uniaxial Magnet in the Higher Non-Gaussian Approximation and in the Presence of an External Field

<table>Dependence of quantities <svg height="14.3625" id="M325" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 19.475 14.3625" width="19.475" xmlns="http://www.w3.org/2000/svg">
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<g transform="translate(72,-60.51)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐻</tspan>
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<text transform="matrix(1,0,0,-1,-61.03,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑐</tspan>
</text>
</g>
</g>
</svg> and <svg height="14.3875" id="M326" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 19.862499 14.3875" width="19.862499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.3875)">
<g transform="translate(72,-60.49)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐻</tspan>
</text>
<text transform="matrix(1,0,0,-1,-61.03,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">3</tspan>
</text>
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</g>
</svg> on the ratio <svg height="19.512501" id="M327" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 28.2125 19.512501" width="28.2125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.5125)">
<g transform="translate(72,-56.39)">
<text transform="matrix(1,0,0,-1,-72.38,62.57)">
<tspan style="font-size: 12.50px; " x="0" y="0"></tspan>
<tspan style="font-size: 12.50px; " x="10.69" y="0"></tspan>
<tspan style="font-size: 12.50px; " x="11.12" y="2.9100001">ℎ</tspan>
<tspan style="font-size: 12.50px; " x="0.43000001" y="2.9100001">ℎ</tspan>
<tspan style="font-size: 12.50px; " x="7.6442308" y="2.9100001">/</tspan>
</text>
<text transform="matrix(1,0,0,-1,-54.05,56.53)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑐</tspan>
</text>
</g>
</g>
</svg> for the RG parameter <svg height="11.875" id="M328" style="vertical-align:-0.27588pt" version="1.1" viewbox="0 0 101.975 11.875" width="101.975" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.875)">
<g transform="translate(72,-62.5)">
<text transform="matrix(1,0,0,-1,-71.95,62.83)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑠</tspan>
<tspan style="font-size: 12.50px; " x="8.9646511" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.005039" y="0">𝑠</tspan>
</text>
<text transform="matrix(1,0,0,-1,-45.44,67.83)">
<tspan style="font-size: 8.75px; " x="0" y="0">∗</tspan>
</text>
<text transform="matrix(1,0,0,-1,-36.89,62.83)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="18.279387" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="21.405136" y="0">7</tspan>
<tspan style="font-size: 12.50px; " x="27.656635" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="33.908134" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="40.159637" y="0">9</tspan>
</text>
</g>
</g>
</svg> and the reduced temperature <svg height="14.2" id="M329" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 56.724998 14.2" width="56.724998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2)">
<g transform="translate(72,-60.64)">
<text transform="matrix(1,0,0,-1,-71.95,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜏</tspan>
<tspan style="font-size: 12.50px; " x="9.8648672" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.905256" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="28.156755" y="0">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-37.53,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">−</tspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">4</tspan>
</text>
</g>
</g>
</svg>.</table>

International Scholarly Research Notices

fig3

Figure 3

Figure 3: Free Energy of Three-Dimensional Uniaxial Magnet in the Higher Non-Gaussian Approximation and in the Presence of an External Field 