  This study examines on-shell supersymmetry breaking in the Abelian
$\mathcal{N}=1$ Chern-Simons-matter model within a three-dimensional spacetime.
The classical Lagrangian is scale-invariant, but two-loop radiative corrections
to the effective potential break this symmetry, along with gauge and on-shell
supersymmetry. To investigate this issue, the Renormalization Group Equation is
used to calculate the two-loop effective potential.
