Topological transition in disordered planar matching: combinatorial arcs expansion

Andrey Y. Lokhov 1 Olga V. Valba 2, 3 Sergei K. Nechaev 1, 4, 3 Mikhail V. Tamm 5, 3

Journal of Statistical Mechanics: Theory and Experiment, IOP Science, 2014, pp.P12004

In this paper, we investigate analytically the properties of the disordered Bernoulli model of planar matching. This model is characterized by a topological phase transition, yielding complete planar matching solutions only above a critical density threshold. We develop a combinatorial procedure of arcs expansion that explicitly takes into account the contribution of short arcs, and allows to obtain an accurate analytical estimation of the critical value by reducing the global constrained problem to a set of local ones. As an application to a toy representation of the RNA secondary structures, we suggest generalized models that incorporate a one-to-one correspondence between the contact matrix and the RNA-type sequence, thus giving sense to the notion of effective non-integer alphabets.

  • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
  • 2. N. Semenov Institute of Chemical Physics
  • 3. Department of Applied Mathematics
  • 4. P. N. Lebedev Physical Institute
  • 5. Physics Department