Scale-dependent universality class crossover in magnetic skyrmion polymers
arXiv:2607.26289
The paper investigates one‑dimensional chains of dipolar magnetic skyrmions that act as polymer‑like objects, derives their inter‑skyrmion potential, and shows a scale‑dependent crossover in temperature‑dependent power‑law behavior due to competing interactions.
Abstract
Dipolar magnetic skyrmions can assemble into chains with alternating helicity that act as one-dimensional polymers, yet their statistical mechanics violates the universal harmonic scaling observed in actin, DNA, and microtubules. From first principles, we compute the inter-skyrmion pair potential and find a bi-exponential form of competing interactions with two characteristic decay lengths that encode the distinct microscopic mechanisms of repulsion and attraction. Multiscale simulations reveal a power-law temperature dependence with exponent in the worm-chain limit of a single bond, and exponent in the three-bond limit. We find that the power-law behavior is remarkably independent of magnetic field strength, and the crossover is due to competing radial interactions responsible for the bonds, resulting in a quartic transverse confinement. We show that the precise form of the competing interactions (e.g., Morse or double-Yukawa) does not affect the temperature dependence.
12 pages, 4 figures