The Statistical Properties of Spin-One DKP Oscillator under an External Magnetic Field in Noncommutative Space

<table>The comparison of the Helmholtz free energy<svg height="11.175" id="M133" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 22.025 11.175" width="22.025" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,5.725,11.113)"><path d="M599 650l-18 -160l-30 -2q-2 70 -11 94q-5 16 -26 24t-75 8h-94q-27 0 -33.5 -6.5t-12.5 -32.5l-43 -226h108q52 0 72.5 5t31 18t28.5 52h28l-40 -200h-28q-1 42 -6 56.5t-24.5 21t-70.5 6.5h-108l-32 -177q-13 -65 1 -80.5t88 -22.5l-8 -28h-279l6 28q61 5 77.5 20.5
t29.5 81.5l72 387l7.5 40.5t1 26.5t-4 18t-15.5 10t-24 6t-37 4l8 28h461z" id="x1D439"></path></g>
</svg>for both commutative and noncommutative cases.</table>

Advances in High Energy Physics

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Figure 3

Figure 3: The Statistical Properties of Spin-One DKP Oscillator under an External Magnetic Field in Noncommutative Space 