The radius of a polymer at a near-critical temperature

ABSTRACT

We consider a mean-field model of a polymer with a spherically symmetric finitely supported potential. We describe how the typical size of the polymer depends on the two parameters: the temperature, which approaches the critical value, and the length of the polymer chain, which goes to infinity.

2010 Mathematics Subject Classifications:

• 82B26
• 82B27
• 82D60
• 35K10

Acknowledgments

The work of L. Koralov was supported by the ARO grant W911NF1710419. The work of S. Molchanov was supported by the NSF grant DMS-1714402 and by the Russian Science Foundation, project ${\mathrm{N}}^o$ 17-11-01098 and project ${\mathrm{N}}^o$ 20-11-20119. The work of B. Vainberg was supported by the NSF grant DMS-1714402 and the Simons Foundation grant 527180.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work of L. Koralov was supported by the ARO grant W911NF1710419. The work of S. Molchanov was supported by the NSF grant DMS-1714402 and by the Russian Science Foundation, project ${\mathrm{N}}^o$ 17-11-01098 and project ${\mathrm{N}}^o$ 20-11-20119. The work of B. Vainberg was supported by the NSF grant DMS-1714402 and the Simons Foundation grant 527180.