What is the physics behind showing a spin glass state in a geometrically frustrated magnetic system? And if it is not the case for all the magnetically frustrated system then why?
A spin glass system is an alloy. It exhibits spin glass behaviour depending on the concenration of the magnetic atoms, e.g. CuMn for 0.1% Cu, FexZn1-xF2 for x
Well for the spin glass you have to be careful about the ingredients of this case such as anisotropy, frustration, and competing interaction. Only frustration cant do that. I would like you to go through the book by Mydosh on spin glass.
As My answer is "No". According to the J. Mydosh's textbook on spin glass, the randomness in exchange interaction coming from defects, disorders, bond disorder, and etc. seems to be a key factor to derive the spin glass state out of the situation of geometrically frustrated magnetic interaction. Even without the GFM, the randomness in spin exchange interaction should be one of main causes for a spin glass state.