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August 2018 Critical parameter of random loop model on trees
Jakob E. Björnberg, Daniel Ueltschi
Ann. Appl. Probab. 28(4): 2063-2082 (August 2018). DOI: 10.1214/17-AAP1315

Abstract

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.

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Jakob E. Björnberg. Daniel Ueltschi. "Critical parameter of random loop model on trees." Ann. Appl. Probab. 28 (4) 2063 - 2082, August 2018. https://doi.org/10.1214/17-AAP1315

Information

Received: 1 October 2016; Revised: 1 March 2017; Published: August 2018
First available in Project Euclid: 9 August 2018

zbMATH: 06974745
MathSciNet: MR3843823
Digital Object Identifier: 10.1214/17-AAP1315

Subjects:
Primary: 60K35, 82B20, 82B26, 82B31

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.28 • No. 4 • August 2018
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