I have defined a function the energy $E$ of a given system by
f1[A_,α_,γ_,κ_,V0_,σ_,Rc_,k_]:=(π*A^2)/(2*k)+(π*γ*σ^2)/α (A^2+PolyLog[2,-A^2α]/α)+((π^2)*(σ^4)*κ*(A^4)*V0 )/2+(Sqrt[2π]*π^2*σ^5*κ*A^4*V0)/(4Rc) Exp[σ^2/(2Rc)](-1+Erf[σ/(Sqrt*Rc)])
After fixing the values of $A,\alpha,V0,Rc$ and $k$, I want to find the values of $\sigma$ that makes $E$ minimum while varying $\gamma$ and $\kappa$. Finally, I would like to make a density plot of the results obtained.
The question is, how can this be done?
In my attempts to solve the problem, I fixed some values for the variables aforementioned. Next, I created a Table under the name mf, which stores the $f[\gamma,\kappa,\sigma]$ for $\gamma$ and $\kappa$ varying from $(-100,0)$ and $(0,100)$, respectively.
In what follows, I was thinking of minimizing each of the elements of mf with respect to $\sigma$ and finally, make the plot. I even tried to implement it but it didn't work out. I am probably making mistakes.