Critical parameter of random loop model on trees

@article{Bjornberg2018CriticalPO,
  title={Critical parameter of random loop model on trees},
  author={Jakob E. Bjornberg and Daniel Ueltschi},
  journal={Annals of Applied Probability},
  year={2018},
  volume={28},
  pages={2063-2082}
}
  • Jakob E. Bjornberg, Daniel Ueltschi
  • Published 2018
  • Mathematics, Physics
  • Annals of Applied Probability
  • We give estimates of the critical parameter for random loop models that are related to quantum spin systems. A special case of the model that we consider is the interchange- or random-stirring process. We consider here the model defined on regular trees of large degrees, which are expected to approximate high spatial dimensions. We find a critical parameter that indeed shares similarity with existing numerical results for the cubic lattice. In the case of the interchange process, our results… CONTINUE READING

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