Local defect in a magnet with long-range interactions

TL;DR

This paper studies how a local defect affects droplet formation in a nearly critical magnet with long-range interactions, revealing that long-range tails are subleading for positive , making the behavior similar to short-range cases, with implications for quantum ferromagnets.

Contribution

It demonstrates that long-range interactions do not alter the leading order droplet free energy for positive , extending understanding of defect-induced phenomena in critical magnets.

Findings

Long-range tails are subleading for >0, making droplet free energy similar to short-range cases.

Droplet quantum dynamics are analyzed with and without dissipation.

Results have implications for defects in itinerant quantum ferromagnets.

Abstract

We investigate a single defect coupling to the square of the order parameter in a nearly critical magnet with long-range spatial interactions of the form $r^{-(d+\sigma)}$, focusing on magnetic droplets nucleated at the defect while the bulk system is in the paramagnetic phase. Because of the long-range interaction, the droplet develops a power-law tail which is energetically unfavorable. However, as long as $\sigma>0$, the tail contribution to the droplet free energy is subleading in the limit of large droplets; and the free energy becomes identical to the case of short-range interactions. We also study the droplet quantum dynamics with and without dissipation; and we discuss the consequences of our results for defects in itinerant quantum ferromagnets.