There are some, but technically he could do it:
www.pbs.org
TLDR: The President could order an attack on his own, but that order has to be passed down to people below him. Odds are that a key person would balk at such an order, but if that did not happen . . . BOOM!!
Which is why I can understand your concerns about him being head of state.
Of course one thing that should comfort you is that Trump could tell that the military would not follow his orders if he tried to declare martial law after losing. They made that clear to him, so I think that you probably, please not I said probably, be safe from the US shooting off missiles on just the President's wishes.