expansion analysis of very weak first-order transitions in the cubic anisotropy model: Part I

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The cubic anisotropy model provides a simple example of a system with an arbitrarily weak first-order phase transition. We present an analysis of this model using -expansion techniques with results up to next-to-next-to-leading order in. Specifically, we compute the relative discontinuity of various physical quantities across the transition in the limit that the transition becomes arbitrarily weakly first-order. This provides a useful test-bed for the application of the expansion in weakly first-order transitions.