Extreme graphical glitches when playing Minecraft in 4K with default memory limit

I just installed Java JDK & JRE 6u45 and 7u72 to be able to develop Java apps and mod the game. I proceeded to download Minecraft, and as I had gotten a new computer, I decided to check out how well the game would run on it.

After downloading, logging in, etc., I created a new world, and went to video settings. I set everything to high, fancy etc. to test a little, Turned out that selecting a very high render distance made the entire world flicker with graphical glitches. I loaded Fraps, and decided to record this as a bug report.

Messing around with the settings, I tried to figure out whether reducing render distance would help, and indeed it did. I tried adjusting it higher, and once I reached 29 or so, I started experiencing the graphical glitches again, though this time, it only happened on parts of the world. You can see this in the video I've attached further down in the report. After walking around a little, I took a look in the top-right corner and saw the memory usage going up and down between 700 and 900 MB about twice per second, and figured it might have something to do with the problem. So I stopped recording, and exited the game. I also took a backup of logs/latest.txt (uploaded here). I re-entered the launcher, and edited the profile (the default one, named by my username) and

• Set launcher to always be displayed

• Enabled JVM arguments and *changed -Xmx1G to -Xmx4G".

I proceeded to launch the game, and now the flickering blocks were gone, even at maximum render distance.

This leads me to believe that the default memory limit in the launcher (1 GB) is too small for playing on a ultra high-res display.

Attached is the log file from when the game glitched.
A video of the glitch in effect (upscaled to 2160p from 2097p for YouTube purposes) can be found at this YouTube link.

This is the first time I run Minecraft on this computer.