Mean-field tricritical polymers

Abstract: We provide a full description of a tricritical phase diagram in the setting of a mean-field random walk model of a polymer density transition. The model involves a continuous-time random walk on the complete graph in the limit as the number of vertices N in the graph grows to infinity. The walk has a repulsive self-interaction, as well as a competing attractive self-interaction whose strength is controlled by a parameter g. A chemical potential ν controls the walk length. We determine the phase diagram in the (g,ν) plane, as a model of a density transition for a single linear polymer chain. The proof uses a supersymmetric representation for the random walk model, followed by a single block-spin renormalisation group step to reduce the problem to a 1-dimensional integral, followed by application of the Laplace method for an integral with a large parameter. The talk is based on joint work with Roland Bauerschmidt, Probability and Mathematical Physics 1, 167-204 (2020); arXiv:1911.00395 .

mathematical physics

Audience: researchers in the discipline

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