Mac hardware for 4k/uhd?



I've been using a mac mini as Plex Server for a few years now and I tried to play back some UHD/4k releases but had constant stutter/lag.

So, my question, will a new mac mini manage playback 4k/uhd material?

Current specs:
Mini 2012
2,5Ghz i5,
Intel HD Graphic 4000

New specs for mini:
1,4Ghz i5 (whaaa?) OR 2,6Ghz i5
Intel HD Graphic 5000 OR Intel Iris Graphics (is any of them enough for 4k?)

If none of them is enough, what alternatives do I have in the pc-world? I need a machine that does not make any noise more or less, just like a mini.