The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 28, Number 4 (2018), 2063-2082.
Critical parameter of random loop model on trees
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 improve on earlier work by Angel and by Hammond, in that we determine the second-order term of the critical parameter.
Ann. Appl. Probab., Volume 28, Number 4 (2018), 2063-2082.
Received: October 2016
Revised: March 2017
First available in Project Euclid: 9 August 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs 82B26: Phase transitions (general) 82B31: Stochastic methods
Björnberg, Jakob E.; Ueltschi, Daniel. Critical parameter of random loop model on trees. Ann. Appl. Probab. 28 (2018), no. 4, 2063--2082. doi:10.1214/17-AAP1315. https://projecteuclid.org/euclid.aoap/1533780267