Battlefield is a borderline case. It utilizes four cores quite well, but the performance gain is so small that you can reach similar results with a highly overclocked dual-core CPU. Overclocking results in a small frame rate increase, as well as slightly lower CPU utilization.
With AA enabled, the game uses up to 700 MB of graphics memory.
For higher frame rates, you need to overclock a dual-core CPU or use a quad-core CPU and then upgrade the graphics card. Using a single-core CPU will severely limit performance.