Get Temperature Monitor to see if it's heat related...
Does it use Flash or Java?
One way to test is to Safe Boot from the HD, (holding Shift key down at bootup), run Disk Utility in Applications>Utilities, then highlight your drive, click on Repair Permissions, Test for problem in Safe Mode...
PS. Safe boot may stay on the gray radian for a long time, let it go, it's trying to repair the Hard Drive
Reboot, test again.
If it only does it in Regular Boot, then it could be some hardware problem like Video card, (Quartz is turned off in Safe Mode), or Airport, or some USB or Firewire device, or 3rd party add-on, Check System Preferences>Accounts>Login Items window to see if it or something relevant is listed.
Check the System Preferences>Other Row, for 3rd party Pref Panes.
Also look in these if they exist, some are invisible...
I restarted mac Mini 2012 while im holding a shift key, it didn't happen...
I believe i'm having similiar problem to this topic, i get randomly blackouts while im using an app.
wow, i didn't know Mac Mini 2012 has a defective video card.
Does it work in international operation?
I have no physic invoice, but i got a digital invoice from Amazon.
Amazon says After the applicable return period has expired, your item might still be eligible for exchange or repair under the manufacturer's warranty. To determine if your item is eligible for a warranty return, review the paperwork that came with the merchandise or contact the manufacturer. Please note, that in order for an item to be eligible for warranty coverage, many manufacturers require the item to be purchased from an authorized dealer. Amazon.com and seller may not be an authorized dealer for all items they sell. If you are in doubt, you can confirm that a seller is an authorized dealer by contacting the manufacturer.
Anyways, i'm going to call Apple official store
joannesalfa - if you have an Apple store near you, make a Genius bar appointment and they should help you - no matter where you bought it, as long as it's within the first year. Indeed, because of Apple's excellent service they are one of the few vendors I will bother buying an extended warranty (AppleCare) from. If you don't have an Apple Store near you it's not quite as handy, but they still provide excellent support over the phone/by mail if need be too.