I have a constant 600+ FPS when I run Minecraft. Because of that, my computer became very hot, and I decided to intall OptiFine and limit the framerate with Vsync to 70 FPS. This problem, however, occurs both when OptiFine disabled and vsync enabled and disabled.

I get a lot lag spikes at random.
I looked at the F3 menu, and noticed that I used 100% of the allocated RAM, which explained the lag spikes. Therefor I decided to allocate more RAM to Minecraft by going to "Edit Profile" (in the Minecraft Launcher 1.6.11), and in the JVM Arguments, I added this line: -Xmx4096M -XX:+UseConcMarkSweepGC -XX:+CMSIncrementalMode -XX:-UseAdaptiveSizePolicy -Xmn4096M

With this, I should have allocated 4GB of RAM to Minecraft, but when I go to Minecraft and look at the F3 menu, I only have 1843 MB of RAM. I then allocated 4096 MB (4 GB) of RAM to Java, but did not help at all.

Look at the attached image. In the lower left corner you can see the FPS. The orange line is the lag spike I get.

What is the problem? I have searched everywhere on Google, tried every solutions I found; nothing worked though.

EDIT:
When playing with the F3 menu open, I see that "Mem" (upper right corner) keeps rising until it gets to 100%, then the lag spike occurs, and then it resets to 0%