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Building on our earlier work (Saeedian et al. 2018), we introduce and study generalized XX0 models. We explicitly construct a long-range interacting spin chain, referred to as the Selberg model, and study the correlation functions of the Selberg and XX0 models. Using a matrix integral representation of the generalized XX0 model and applying asymptotic analysis in non-intersecting Brownian motion, the phase structure of the Selberg model is determined. We find that tails of the TracyâWidom distribution, of Gaussian unitary ensemble, govern a discrete-to-continuous third-order phase transition in Selberg model. The same method also reproduces the GrossâWitten phase transition of the original XX0 model. Finally, we conjecture universal features for the phase structure of the generalized XX0 model.
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