H1z1 Minimum specs are
CPU: Intel i3 Dual-Core with Hyper-Threading (required)
RAM: 4 GB
OS: Windows 7 64-bit
Video Card: nVidia GeForce GTX 275 series or higher
Free Disk Space: 20 GB
Recommended are:
CPU: Intel i5 Quad Core or higher / AMD Phenom II X6 or higher
RAM: 8 GB
OS: Windows 7 64-bit
Video Card: nVidia GeForce GTX 560 series or higher / AMD Radeon HD 6870 or higher
Free Disk Space: 20 GB
I think recommended specs are for Medium to High settings.