Thermal Properties of Vortices on Curved Surfaces

TL;DR

This study uses Monte Carlo simulations to investigate how curvature influences vortex behavior and long-range order in the XY model on curved surfaces, revealing that high curvature induces unbounded vortices and destroys order.

Contribution

It demonstrates that surface curvature significantly affects vortex proliferation and correlation decay in XY models, challenging assumptions about geometry's role in these systems.

Findings

Curvature does not affect vortex proliferation compared to flat surfaces.

High curvature leads to unbounded vortices at low temperatures.

Long-range order diminishes with increasing curvature.

Abstract

We use Monte Carlo simulations to study the finite temperature behavior of vortices in the XY- model for tangent vector order on curved backgrounds. Contrary to naive expectations, we show that the underlying geometry does not affect the proliferation of vortices with temperature respect to what is observed on a flat surface. Long-range order in these systems is analyzed by using the classical two-point correlation functions. As expected, in the case of slightly curved substrates these correlations behave similarly to the plane. However, for high curvatures, the presence of geometry-induced unbounded vortices at low temperatures produces the rapid decay of correlations and an apparent lack of long-range order. Our results shed light on the finite-temperature physics of soft-matter systems and anisotropic magnets deposited on curved substrates.