Critical behavior of magnetic polymers on the three-dimensional Sierpinski Gasket

We present the (numerically) exact phase diagram of a magnetic polymer on the Sierpinsky gasket embedded in three dimensions using the renormalization group method. We report distinct phases of the magnetic polymer, including paramagnetic swollen, ferromagnetic swollen, paramagnetic collapsed, and ferromagnetic collapsed states. By evaluating critical exponents associated with phase transitions, we located the phase boundaries between different phases. If the model is extended to include a four-site interaction which disfavors configurations with a single spin of a given type, we find a rich variety of critical behaviors. Notably, we uncovered a phenomenon of reentrance, where the system transitions from a collapsed (paramagnetic) state to a swollen (paramagnetic) state followed by another collapse (paramagnetic) and ultimately reaching a ferromagnetic collapsed state. These findings shed new light on the complex behavior of (lattice) magnetic polymers.

Automated summary

In this study, we obtained the (numerically) exact phase diagram of a magnetic polymer on the Sierpinsky gasket embedded in three dimensions using the renormalization group method. We observed distinct phases and phase boundaries between them. By including a four-site interaction in the model, we discovered rich critical behaviors, including the phenomenon of reentrance between collapsed and swollen states of the magnetic polymer.