Brewer, Richard C.Owen, Evan2025-02-032025-02-032023https://hdl.handle.net/2144/496772023I derive a formulation of the 2-dimensional critical Ising model on non-uniform simplicial lattices. Surprisingly, the derivation leads to a set of geometric constraints that a lattice must satisfy in order for the model to have a well-defined continuum limit. I perform Monte Carlo simulations of the critical Ising model on discretizations of several non-trivial manifolds including a twisted torus and a 2-sphere and I show that the simulations are in agreement with the 2d Ising CFT in the continuum limit. I discuss the inherent benefits of using non-uniform simplicial lattices to study quantum field theory and how the methods developed here can potentially be generalized for use with other theories.en-USAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/PhysicsConformal field theoryIsing modelLattice field theoryMonte CarloThesis/Dissertation2025-01-300000-0003-4200-9778