We consider two intimately related statistical mechanical problems on : (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 .
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March 2020
Research Article|
March 10 2020
Three-dimensional tricritical spins and polymers
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Roland Bauerschmidt
;
Roland Bauerschmidt
a)
1
Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge
, Wilberforce Road, Cambridge CB3 0WB, United Kingdom
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Martin Lohmann
;
Martin Lohmann
b)
2
Department of Mathematics, University of British Columbia
, Vancouver, British Columbia V6T 1Z2, Canada
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Gordon Slade
Gordon Slade
c)
2
Department of Mathematics, University of British Columbia
, Vancouver, British Columbia V6T 1Z2, Canada
c)Author to whom correspondence should be addressed: [email protected]
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Roland Bauerschmidt
1,a)
Martin Lohmann
2,b)
Gordon Slade
2,c)
1
Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge
, Wilberforce Road, Cambridge CB3 0WB, United Kingdom
2
Department of Mathematics, University of British Columbia
, Vancouver, British Columbia V6T 1Z2, Canada
a)
E-mail: [email protected]
b)
E-mail: [email protected]
c)Author to whom correspondence should be addressed: [email protected]
J. Math. Phys. 61, 033302 (2020)
Article history
Received:
May 16 2019
Accepted:
February 05 2020
Citation
Roland Bauerschmidt, Martin Lohmann, Gordon Slade; Three-dimensional tricritical spins and polymers. J. Math. Phys. 1 March 2020; 61 (3): 033302. https://doi.org/10.1063/1.5110277
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