Microscopic phase coexistence: a conformal bootstrap analysis

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A new non-perturbative, numerical technique, the 'conformal bootstrap', has been developed for constraining and solving conformal field theories. The method has recently been used to predict the critical exponents of the 3D Ising model to a greater precision than any method ever used.In my project, the conformal bootstrap will be applied to systems in which there are two competing phases at low-temperature. We will attempt to investigate the case where both phases have O(2) symmetry, exploring whether there is a first-order transition from one phase to the other, or whether a range of parameters describe the coexistence of the phases.With this established, we'll then proceed to investigate the non-zero temperature of the systems using the same technique, where one may expect Kosterlitz-Thouless-like phase transitions.