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. To determine the static droplet profile, we solve a Landau-Ginzburg-Wilson action in the saddle-point approximation. 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 consider the effects of fluctuations and find that they do not change the functional form of the droplet as long as the bulk system is noncritical. Finally, we study the droplet quantum dynamics with and without dissipation; and we discuss the consequences of our results for defects in itinerant quantum ferromagnets.




National Science Foundation (U.S.)
Research Corporation

Keywords and Phrases

Defect States; Free Energy; Ferromagnetism; Ising model; Magnetism, Band theory of; Magnetism; Nucleation; Paramagnetism

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

File Type





© 2007 American Physical Society (APS), All rights reserved.

Publication Date

01 Jan 2007

Included in

Physics Commons