The study of convergence of random walks to well defined curves is founded in the fields of complex analysis, probability theory, physics and combinatorics. The foundations of this subject were motivated by physicists interested in the properties of one-dimensional models that represented some form of physical phenomenon. By taking physical models and generalizing them into abstract mathematical terms, macroscopic properties about the model could be determined from the microscopic level. By using model specific objects known as observables, the convergence of the random walks on particular lattice structures can be proven to converge to continuous curves such as Brownian Motion or Stochastic Loewner Evolution as the size of the lattice step approaches 0. This seminar will introduce the field of statistical lattice models, the types of observables that can be used to prove convergence as well as a proof for the q-state Potts model showing that local non-commutative matrix observables do not exist. No prior physics knowledge is required for this seminar.