  The Ising model, often seen as the paradigmatic spin model, has been heavily
studied for its mathematical description of ferromagnetism in statistical
mechanics. We explore a quantum version of this model, the transverse field
Ising model, and investigate how the quantum property of magnetization
fluctuates with geometrical frustration, a phenomenon arising from the geometry
of a spin system's ground state. We introduce a general measure for frustration
and then implement a computational model built in Python that translates spin
lattices into adjacency matrices, solves the spectrum of the transverse field
Ising model, calculates the expected magnetization of the ground state, plots
the variable over randomly generated spin systems with controllable degrees of
geometrical frustration, and compares the evolution of these plots over an
increasing transverse field. Our finite-size studies exhibit an expected
decrease in magnetization with increasing frustration and suggest the
possibility of robust phases in the large N limit over finite ranges of
frustration, which may be precursors to spin liquids or spin glasses.
