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    $\begingroup$ This works (i diveded function energy by 10^10 to help FindMinimum) Manipulate[ Plot[\[Sigma] /. FindMinimum[ Rationalize[ energy[7*10^6, \[Sigma], 8.055*10^6, 0.0000659176, p, \[CapitalDelta], 1], 0]/10^10, {\[Sigma], .01, 10}, MaxIterations -> 500, PrecisionGoal -> 5, WorkingPrecision -> 20][[2]], {p, 0, 10}], {\[CapitalDelta], 10^-6, 1000, Appearance -> "Labeled"}] $\endgroup$ Commented Nov 3, 2020 at 3:15
  • $\begingroup$ @Akku14 thanks! Just two additional questions. First, what is the necessity of Rationalize in your answer? Second, how to get rid of the errors related with replacement and reps being suppressed during calculation? I am getting those when running what you provided so Manipulate has not been working properly. $\endgroup$ Commented Nov 4, 2020 at 20:53
  • $\begingroup$ Your input parameters have MachinePrecision. See Precision[0.0000659176] which is $MachinePrecision about 16, depending an processor. Since i noticed that FindMinimum need higher Precision, i Rationalize the input to infinite precision. Otherwise WorkingPrecision -> 20 wouldn't work. Second, working with version 8.0, id didn't get any error messages. $\endgroup$ Commented Nov 5, 2020 at 5:06