Critical parameter of random loop model on trees
Journal article, 2018

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.

Random loop model

Quantum heisenberg


Jakob Björnberg

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Daniel Ueltschi

The University of Warwick

Annals of Applied Probability

1050-5164 (ISSN)

Vol. 28 4 2063-2082

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Control Engineering



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