I've seen plenty of questions about this, I'm unsure whether it's a lack of processing power or something with Elementary OS.
I am not sure what to look for in any logs. I'm dual booting Windows 10 and Elementary OS 0.3.2 Freya (64-bit).
Processor: Quad-Core AMD A8-7410 APU with AMD Radeon R5 Graphics Memory: 3.3 GiB Graphics: Advanced Micro Devices, Inc. [AMD/ATI] Mullins [Radeon R4/R5 Graphics] (rev 45) Storage: 165.0 GB
My laptop is a HP 15z-af100.
If you need any log data or something let me know, I can reproduce this by simply trying to apt-get upgrade my GTK theme.
EDIT - Not related to the theme, tried installing a package and it also froze (install via a .deb file).
Easy for me to reproduce. I can't get into Ctrl-Alt-F1 or F2. I can only shut up manually or with Ctrl+Alt+SysRq+B.