2009/08/07 by Constantin Candu, C. Candu, J. L. Jacobsen +7
Computer Science · Physics and Astronomy · #Computational Drug Discovery Methods #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Topological and Geometric Data Analysis #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.0908.1081
5 pages
arxiv created 2009/08/07 · openalex publication_date 2009/08/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the usual statistical model of a dense polymer (a single space-filling loop on a lattice) in two dimensions the loop does not cross itself. We modify this by including intersections in which \em three lines can cross at the same point, with some statistical weight w per crossing. We show that our model describes a line of critical theories with continuously-varying exponents depending on w, described by a conformally-invariant non-linear sigma model with varying coupling constant gσ2 >0. For the boundary critical behavior, or the model defined in a strip, we propose an exact formula for the ℓ-leg exponents, h_ℓ=gσ2 ℓ(ℓ-2)/8, which is shown numerically to hold very well.