Spin dynamics simulation of the three-dimensional XY model: Structure factor and transport properties

TL;DR

This paper uses advanced Monte Carlo spin dynamics simulations to analyze the structure factor and transport properties of the 3D XY model, revealing spin wave behavior, dynamic scaling violations, and transport coefficients near criticality.

Contribution

It introduces an efficient integration algorithm enabling detailed analysis of spin dynamics, including structure factors and transport properties, in the 3D XY model.

Findings

Spin wave peaks observed around the critical point.

Evidence of dynamic scaling violation at criticality.

Agreement of dispersion relations with mode coupling theory.

Abstract

We present extensive Monte-Carlo spin dynamics simulations of the classical XY model in three dimensions on a simple cubic lattice with periodic boundary conditions. A recently developed efficient integration algorithm for the equations of motion is used, which allows a substantial improvement of statistics and large integration times. We find spin wave peaks in a wide range around the critical point and spin diffusion for all temperatures. At the critical point we find evidence for a violation of dynamic scaling in the sense that independent components of the dynamic structure factor S(q,w) require different dynamic exponents in order to obtain scaling. Below the critical point we investigate the dispersion relation of the spin waves and the linewidths of S(q,w) and find agreement with mode coupling theory. Apart from strong spin wave peaks we observe additional peaks in S(q,w) which can be attributed to two-spin wave interactions. The overall lineshapes are also discussed and compared to mode coupling predictions. Finally, we present first results for the transport coefficient D(q,w) of the out-of-plane magnetization component at the critical point, which is related to the thermal conductivity of He4 near the superfluid-normal transition.