I think this is an in game issue as it used to do that with me, have you done all the updates and patches ?
These are the recommended specs and yours way beats these so it should not be a hardware issue.
32Mb video card (Geforce equiv.)
Direct X 8.1 or higher
Direct X compatible sound card
56K Modem for Internet access
Have you closed all background applications that could be using the CPU/Memory. for example i keep my outlook running while playing games but i have noticed that outlook uses a lot of memory. Also web explorers use high amounts of memory.
My sugestion is to make sure everything is closed before running the game (open task manager and sort by the most use on CPU and Memory). you could also try running the game on the lowest possible settings to see if that makes a difference. also download and install Fraps
which will tell you your frames per second during the game and during these hiccups your having.
Report back with the results.