Conformational phase transitions in models of magnetic polymers

Magnetic polymers, where each monomer carries a magnetic moment or spin, are a class of interacting polymers that have recently received much attention from the polymer and statistical mechanics community. The reason is at least twofold: (i) they have several applications in material science and (ii) from statistical mechanics perspective they are nice examples of interacting systems where the entropy of the polymer substrate and the magnetic interaction energy between spins can give rise to rich equilibrium phase diagrams and nonstandard critical phenomena. Moreover, recently they have been successfully exploited to understand how the interplay between chromatin (the polymer) folding and epigenetic landscape (the spins) can contribute to shaping the genome organization in the nuclei. In this thesis, I extended previously investigated models of Ising or Potts-like magnetic polymers to the case in which the underlying magnetic system can, if embedded in regular space, display multicritical behaviors. In particular, I considered the Blume-Emery-Grifftih model where vacancies (i.e. sites with no magnetic moment) are considered. On a regular square lattice, a tricritical point between a critical line and line of first-order phase transition occurs. Using mean-field approximations and Monte Carlo simulations of a lattice polymer model, I looked at how the equilibrium phase diagram and the corresponding phase transitions can be shaped by the magnetic interactions, exploring, in particular, the role of the tricritical point on the configurational properties of the polymeric substrate. Strikingly, a mean-field compact disordered phase emerges, that was previously obtained only by driving the system out of equilibrium or by including an overall attractive contribution.