A short proof of the discontinuity of phase transition in the planar random-cluster model with $q>4$

@article{Ray2019ASP,
  title={A short proof of the discontinuity of phase transition in the planar random-cluster model with \$q>4\$},
  author={G. Ray and Yinon Spinka},
  journal={arXiv: Probability},
  year={2019}
}
  • G. Ray, Yinon Spinka
  • Published 2019
  • Mathematics, Physics
  • arXiv: Probability
  • The goal of this paper is to provide a short proof of the discontinuity of phase transition for the random-cluster model on the square lattice with parameter $q>4$. This result was recently shown via the so-called Bethe ansatz for the six-vertex model. Our proof also exploits the connection to the six-vertex model, but does not rely on the Bethe ansatz. Our argument is soft and only uses very basic properties of the random-cluster model (for example, we do not need the Russo--Seymour--Welsh… CONTINUE READING

    Figures from this paper.

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 21 REFERENCES
    On the random-cluster model: III. The simple random-cluster model
    91
    On the transition between the disordered and antiferroelectric phases of the 6-vertex model.
    9
    First-order phase transitions in large entropy lattice models
    88
    Equivalence of the Potts model or Whitney polynomial with an ice-type model
    110
    Phases coexistence and surface tensions for the potts model
    57