Conformational and Magnetic Order in XY Spin-Decorated Polymers

Magnetic polymers, macromolecules composed of monomers carrying a magnetic spin, are minimal models for responsive, smart materials and for chromatin organization, elegantly combining 3D folding and 1D epigenetic spreading. The interest in these systems stems from the coupling between the magnetic and conformational degrees of freedom, as spins carried by monomers that occupy nearest-neighbor lattice sites interact, regardless of their separation along the chain. Magnetic alignment can consequently favor configurations with many lattice contacts, while the resulting effective attraction can promote polymer collapse. In this thesis, we extend the magnetic polymer model from discrete Ising spins to spins with a generic O(n) symmetry, focusing on the O(2) (XY) and O(3) cases. We combine a mean-field treatment of the equilibrium phase diagram with Markov chain Monte Carlo simulations of three-dimensional XY and O(3) magnetic polymers and of a two-dimensional XY magnetic polymer, also examining the effects of an external homogeneous magnetic field. Mean-field theory predicts the same qualitative phase diagram for all O(n) models: a low-field first-order transition line and a high-field continuous transition line meet at a tricritical point. At fixed field, the transition temperature decreases as the spin dimensionality n increases. The three-dimensional simulations support first-order transitions at zero field, whereas the finite-field behavior is compatible with continuous transitions over the simulated polymer sizes and external fields. The two-dimensional XY magnetic polymer instead undergoes a continuous collapse transition whose finite-size behavior differs from the BKT transition of the fixed-lattice model, although the magnetic and structural estimators leave open the possibility of distinct magnetic and conformational phenomena.