Simulation shows my op Amp has a gain for infinite frequency spectrum
The model is too simple. More specifically, the MOSFET models are too simple. Spice models like these don't have any built in bandwidth limits (how could they?), unless you add them. More realistic FETs will have values defined for CGD0 and CGS0. With those in place you'd find high frequency poles to roll off the gain. 

But, you can learn a lot with simple models like this. Even models that are too simple. It allows you to look at the effects of some single thing in isolation. 

In this case there is one part to limit bandwidth, C1, the Miller capacitor. So, you can see, in isolation, how Miller feedback works. Miller feedback is the most common method of compensating an OpAmp. 

Looking at the Bode plot, you can see the low frequency pole provided by Miller feedback. But, at about 5MHz, you also see a zero, that causes the gain to flatten out. It's a special kind of zero. What kind of zero causes loss of phase? 

Anyway, simple Miller feedback like this is, always provides a low frequency pole and that funny acting zero that makes the OpAmp loose phase.