Critical parameter of random loop model on trees
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 randomstirring 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 secondorder term of the critical parameter.
 Publication:

arXiv eprints
 Pub Date:
 August 2016
 arXiv:
 arXiv:1608.08473
 Bibcode:
 2016arXiv160808473B
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 60K35;
 82B20;
 82B26;
 82B31
 EPrint:
 14 pages, 5 figures