Unwinding Scaling Violations in Phase Ordering

Abstract

The one-dimensional $O(2)$ model is the simplest example of a system with topological textures. The model exhibits anomalous ordering dynamics due to the appearance of two characteristic length scales: the phase coherence length, $L\sim t^{1/z}$, and the phase winding length, $L_w\sim L^{\chi }$. We derive the scaling law $z=2+\mu \chi$, where $\mu =0$ ($\mu =2$) for nonconserved (conserved) dynamics and $\chi =1/2$ for uncorrelated initial orientations. From hard-spin equations of motion, we consider the evolution of the topological defect density and recover a simple scaling description. (please email [email protected] for a hard copy by mail)

4 pages, LATeX, uuencoded figure file appended: needs epsf.sty, [resubmitted since postscript version did not work well], M/C.TH.94/21,NI94022

References in corpus (3)

• Theory of Phase Ordering Kinetics
• Phase Ordering of 2D XY Systems Below T_{KT}
• Scaling Violations with Textures in Two-Dimensional Phase-Ordering

Cited by in corpus (16)

• Spatial organization in cyclic Lotka-Volterra systems
• The Energy-Scaling Approach to Phase-Ordering Growth Laws
• Dynamical Scaling: the Two-Dimensional XY Model Following a Quench
• Bi-directional universal dynamics in a spinor Bose gas close to a non-thermal fixed point
• Violation of single-length scaling dynamics via spin vortices in an isolated spin-1 Bose gas
• Slow Coarsening in an Ising Chain with Competing Interactions
• Dynamical Scaling In Two Dimensional Quenched Uniaxial Nematic Liquid Crystals
• Dynamical Multiscaling in Quenched Skyrme Systems
• Phase ordering and universality for continuous symmetry models on graphs
• Crossover between Ising and XY-like behavior in the off-equilibrium kinetics of the one-dimensional clock model
• Chiral Phase Transition and Baryon Number Conservation
• Complex phase-ordering of the one-dimensional Heisenberg model with conserved order parameter
• Formation of extended topological defects during symmetry breaking phase transitions in O(2) and O(3) models
• Corrections to Scaling in the Phase-Ordering Dynamics of a Vector Order Parameter
• Structure-Factor Tail for the Ordering Kinetics of Nonconserved Fields without Topological Defects
• Reaction Zones and Quenched Charged-Particle Systems with Long-Range Interactions