A new look at the collapse of two-dimensional polymers

作者：Vernier Eric^*; Jacobsen Jesper Lykke; Saleur Hubert

来源：Journal of Statistical Mechanics: Theory and Experiment , 2015, 2015(9): P09001.

DOI：10.1088/1742-5468/2015/09/P09001

• conformal field theory
• loop models and polymers
• classical Monte Carlo simulations

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, Theta(BN) and Theta(DS), 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 Theta(BN) 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 Theta(BN) 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 Theta(BN) and examine the flow along the multicritical line between Theta(BN) and Theta(DS).

• 出版日期2015-9
• 单位中国地震局