Novel phase transition in two-dimensional xy-models with long-range interaction

Abstract

The purpose of this article is to give an overview of results concerning ordering and critical properties of two-dimensional ferromagnets including the dipolar interaction. We investigate a two-dimensional xy-model extended by the dipolar interaction. Describing our system by a nonlinear σ-model and using renormalization group methods we predict a phase transition to an ordered state. This transition is due to the long-range dipolar interaction. The ferromagnetic phase is governed by a low temperature fixed-point with infinite dipolar coupling. In the critical regime we find exponential behavior for the correlation length and the order parameter in contrast to the usual power laws. The nature of the transition shows a striking similarity to the Kosterlitz-Thouless transition. We show that there is a whole class of longrange xy-models leading to such non-standard behavior. Parameterizing the divergencies in terms of the correlation length we are able to calculate the critical exponents. These exponents are correct in any loop order.

Emergent Berezinskii-Kosterlitz-Thouless Phase in Low-Dimensional Ferroelectrics

“…Indeed, it is well known that the dipolar interaction tends to stabilize the long-range order against thermal fluctuations, and the ground state may thus be spontaneously polarized [14,15], or acquire various structures. However, while the low temperature properties substantially depend on the dipolar interaction, in the high temperature regime this interaction is of a lesser significance [16], and its contribution demonstrated to be irrelevant in the treatment of the dipolar XYmodel [13,[15][16][17][18]. Furthermore, in an anisotropic variant of the two-dimensional XY-model with short-range interactions [19,20], it was found that the introduction of a small effective anisotropy had no effect in altering the BKT transition.…”

“…In these systems, the presence of a dipole-dipole interaction, nonlocal in nature, significantly reduces fluctuations, thereby altering the low-temperature properties of the XY-model [13]. Indeed, it is well known that the dipolar interaction tends to stabilize the long-range order against thermal fluctuations, and the ground state may thus be spontaneously polarized [14,15], or acquire various structures.…”