Worried about purple and blue tang

[GTAaquarist]

So I have a 120 gallon reef tank and I just added a purple 2 days ago and had a blue in there before the blue is about 2 inches and purple about 3 so far there has been no fighting or anything like that but sometimes the blue will retreat back to its little area when it swims to far into the purples territory and the purple will sort of scare it a little and tell it it's his territory. I'm just worried that this might turn into fighting or aggression towards the new fish. Again there's no ripping fins or biting at all just what I describes. Your input would be really appreciate just want to make sure that my fish are all happy.
Thanks Dimitri

 

[Politiceaux]

So I have a 120 gallon reef tank and I just added a purple 2 days ago and had a blue in there before the blue is about 2 inches and purple about 3 so far there has been no fighting or anything like that but sometimes the blue will retreat back to its little area when it swims to far into the purples territory and the purple will sort of scare it a little and tell it it's his territory. I'm just worried that this might turn into fighting or aggression towards the new fish. Again there's no ripping fins or biting at all just what I describes. Your input would be really appreciate just want to make sure that my fish are all happy.
Thanks Dimitri

To be honest, the tank you have isn't long enough for the purple and is far too short for the blue long term. There will be territorial fighting.