Proof that \(\delta =2\) and \(\beta =1\) under the Triangle Condition

  • Markus HeydenreichEmail author
  • Remco van der Hofstad
Part of the CRM Short Courses book series (CRMSC)


We use the finiteness of the triangle diagram in order to establish that certain critical exponents take on their mean-field values. We again rely on the differential inequalities developed in chapter  3, and complement them with a differential inequality involving the triangle diagram. We then prove that, under the triangle condition, the critical exponents \(\delta \) and \(\beta \) take on their mean-field values \(\delta \) = 2 and \(\beta \) = 1.

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Mathematisches InstitutLudwig-Maximilians-Universität MünchenMünchenGermany
  2. 2.Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands

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