Critical behavior of magnetic polymers on the three-dimensional Sierpiński gasket in the presence of an external magnetic field

We present the critical behavior of a model for a magnetic polymer under an external magnetic field on the three-dimensional Sierpi {n} \'{n}{}sky gasket. Our findings reveal that, at zero magnetic field, the polymer-collapse transition occurs first, followed by a magnetic transition as the temperature is lowered. The first is signaled by a nonzero polymer density with zero magnetization while the second by a spontaneous magnetization. In the presence of a magnetic field the polymer collapses into a magnetized state and there is only one transition. We have mapped the exact phase diagram, identifying the various phases and phase transitions. The model predicts the existence of a reentrance of paramagnetic collapse phase observed even in the absence of a magnetic field. In a limit where only even numbers of spins of each type on an elementary tetrahedron is permitted, we see a stabilization of a paramagnetic-collapsed polymer state against the addition of moderate ferromagnetic field.