Phase diagrams of confined square lattice links

TL;DR

This study uses Monte Carlo simulations to explore phase diagrams of confined dense ring polymers on a square lattice, revealing various equilibrium phases and critical behaviors depending on their linking configurations.

Contribution

It introduces two lattice models of confined ring polymers and characterizes their phase diagrams and critical phenomena through numerical analysis.

Findings

Identification of multiple equilibrium phases

Determination of phase boundary types and critical exponents

Observation of multicritical points where phase boundaries meet

Abstract

We study by Monte Carlo simulations and scaling analysis two models of pairs of confined and dense ring polymers in two dimensions. The pair of ring polymers are modelled by squared lattice polygons confined within a square cavity and they are placed in relation to each other to be either unlinked or linked in the plane. The observed rich phase diagrams of the two models reveal several equilibrium phases separated by first order and continuous phase boundaries whose critical nature depend on this reciprocal placements. We estimate numerically the critical exponents associated with the phase boundaries and with the multicritical points where first order and continuous phase boundaries meet.