Location of the adsorption transition for lattice polymers. (10th January 2017)

• Record Type: Journal Article
• Authors: Madras, Neal
• Is Part Of: Journal of physics. Volume 50:Number 6(2017)
• Publication Date: 2017-01-10
• Subjects: lattice tree -- lattice animal -- self-avoiding walk -- adsorption transition; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa53b7
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We consider various lattice models of polymers: lattice trees, lattice animals, and self-avoiding walks. The polymer interacts with a surface (hyperplane), receiving an energy reward of β for each site in the surface. It is known that there is an adsorption transition at a critical value of β . We present a new proof of the result of Hammersley et al (1982 J. Phys. A: Math. Gen .15 539–71) that the transition occurs at a strictly positive value of β when the surface is impenetrable, i.e. when the polymer is restricted to a half-space. In contrast, for a penetrable surface, it is an open problem to prove that the transition occurs at β = 0 . We reduce this problem to proving that the fraction of N -site polymers whose span is less than N / log 2 ⁡ N is not too small.