Phase diagrams of confined square lattice linked polygons

Abstract

The phase diagrams of two models of two confined and dense two dimensional ring polymers are examined numerically. The ring polymers are placed in a cavity, and are either linked or unlinked in the plane. The phase diagrams are found to be a function of the linking of the polymers, and include multicritical points where first order and continuous phase boundaries meet. We estimate numerically the critical exponents associated with the phase boundaries and the multicritical points.

Critical scaling of lattice polymers confined to a box without endpoint restriction

“…Additionally, our Monte Carlo study reinforces the theoretical framework and exact enumeration analysis in the studies of SAW crossing a square [19][20][21] and finite-size scaling in renormalisation group methods [24]. This work is also timely in relation to recent work on the problem of two self-avoiding polygons confined to a box where there is a different phase diagram if the two polygons are separate, or if one polygon is also contained within the other [25]. Polygon systems where different linking topologies are present are related to polymer knotting [26][27][28][29].…”

“…Our numerical results confirm that the density scales with leading order L −2/3 indicating that α = 1/2 and thus the transition is continuous. We predict that other similar systems, such as confined linked polygons [25], should have this same scaling in the regime where one polymer dominates. In particular, the density exponent should be α = 1/2.…”