Regime--this is the word you use when you are talking about a dictator and their government etc.
This is the word that has to do with the period of time and situation of a ruler/dictator kind of person.
Regiment --Notice there is a "t" there. Now this little word is the one you pick if you are writing about a group of soldiers.
A Regimen--now this word is the one you should use if you are talking about a regular routine or a routine that is going to become regular--you know a dietary regimen or a beauty regimen..etc.
Get it right--or pick a word you know how to use, people!! I see this error all the time and it makes me a bit crazy.