First things first:
The main performance impact for dwarf fortress is CPU single thread performance. This means, that within the same CPU series, it's mainly a question of clock rate, what furthermore means that a Pentium clocked as fast as an i5 of the same generation will have nearly the same performance. Your desktop's processor is from the 2 years old Haswell series (what's actually pretty good), but it's one of the lower clockrate models on the market (3.2 GHz). From the same series there'd be much faster (regarding dwarf fortress) models available, for instance the Pentium G3470 (3.6 GHz), or even faster, the Core i3 4370 (3.8 GHz).
The other main bottleneck of Dwarf Fortress is memory speed. Haswell (officially) only supports memory speeds up to DDR3-1600. There are some mainboards that allow to overclock the memory controller and run memory at higher clock rates, but Intel doesn't guarantee that this works in a stable manner. Without buying new hardware, the only real suggestion I can give is to make sure your memory is actually running in dual channel mode. Memory timings (the latency numbers, that make memory prices go up) should have little, but measurable impact. Usually operating systems try to distribute data in such a way, that those latencies are mitigated, but that's of course not always possible.
(Side note: Intel Skylake supports much higher memory clock rates when using DDR4, but that'd require a new processor and mainboard...)
Another impact would theoretically be processor cache. But as dwarf fortress uses huge amounts of memory, one would need a gigantic cache (hundreds of MB, as available on some way to expensive server processors) to see any significant improvement.
Ah, and you might have noticed I didn't mention AMD. That's because Bulldozer (and derived) AMD processors have horribly low single thread performance. Maybe in 9 months or so AMD will be an option for dwarf fortress again, but until AMD Zen is released: No, just no.
Otherwise, what Shonai_Dweller said, with one exception: Dwarf Fortress can use 4 GB of RAM, but only when being run on 64bit Linux. Not that this would make any difference regarding performance...