A new look at the collapse of two-dimensional polymers. (8th September 2015)

• Record Type: Journal Article
• Authors: Vernier, Éric; Lykke Jacobsen, Jesper; Saleur, Hubert
• Is Part Of: Journal of statistical mechanics. (2015:Sep.)
• Publication Date: 2015-09-08
• Subjects: 1 -- 3; 1/030 -- 1/080 -- 3/030; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2015/09/P09001
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: We study the collapse of two-dimensional polymers, via an O ( n ) model on the square lattice that allows for dilution, bending rigidity and short-range monomer attractions. This model contains two candidates for the theta point, and, both exactly solvable. The relative stability of these points, and the question of which one describes the 'generic' theta point, have been the source of a long-standing debate. Moreover, the analytically predicted exponents of have never been convincingly observed in numerical simulations. In this paper, we shed a new light on this confusing situation. We show in particular that the continuum limit of is an unusual conformal field theory, made in fact of a simple dense polymer decorated with non-compact degrees of freedom . This implies in particular that the critical exponents take continuous rather than discrete values, and that corrections to scaling lead to an unusual integral form. Furthermore, discrete states may emerge from the continuum, but the latter are only normalizable—and hence observable—for appropriate values of the model's parameters. We check these findings numerically. We also probe the non-compact degrees of freedom in various ways, and establish that they are related to fluctuations of the density of monomers. Finally, we construct a field theoretic model of the vicinity of and examine the flow along the multicritical line between and .