Three-dimensional tricritical spins and polymers

Roland Bauerschmidt, Martin Lohmann, Gordon Slade

Research output: Contribution to journalArticlepeer-review


We consider two intimately related statistical mechanical problems on Z3: (i) the tricritical behavior of a model of classical unbounded n-component continuous spins with a triple-well single-spin potential (the |φ|6 model) and (ii) a random walk model of linear polymers with a three-body repulsion and two-body attraction at the tricritical theta point (critical point for the collapse transition), where repulsion and attraction effectively cancel. The polymer model is exactly equivalent to a supersymmetric spin model, which corresponds to the n = 0 version of the |φ|6 model. For the spin and polymer models, we identify the tricritical point and prove that the tricritical two-point function has Gaussian long-distance decay, namely, |x|-1. The proof is based on an extension of a rigorous renormalization group method that has been applied previously to analyze |φ|4 and weakly self-avoiding walk models on Z4.

Original languageEnglish (US)
Article number033302
JournalJournal of Mathematical Physics
Issue number3
StatePublished - Mar 1 2020

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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