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Paper   IPM / Physic / 16263
School of Physics
  Title:   Exact solvability and asymptotic aspects of generalized XX0 spin chains
1.  M. Saeedian
2.  A. Zahabi
  Status:   Published
  Journal: Physica A: Statistical Mechanics and its Applications
  Vol.:  549
  Year:  2020
  Pages:   124406
  Supported by:  IPM
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 Tracy–Widom distribution, of Gaussian unitary ensemble, govern a discrete-to-continuous third-order phase transition in Selberg model. The same method also reproduces the Gross–Witten 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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