From KPZ Scaling to Long-Lived Solitons in the Classical Heisenberg Chain

Explore the fascinating world of classical spin systems in this 35-minute lecture on the classical Heisenberg chain. Delve into the recently discovered KPZ scaling and its connection to long-lived solitons. Examine the relationship between the non-integrable Heisenberg chain and the integrable Ishimori chain through an interpolating model. Discover the construction of stable stationary solitons and moving soliton solutions in the Heisenberg chain. Investigate the existence regions of single soliton solutions and the renormalization of their properties compared to Ishimori counterparts. Study two-soliton scattering in the Heisenberg chain and observe their survival through multiple scattering events. Learn about the presence of these solitons in thermal states and their implications for the system's dynamics. Gain insights into equilibrium properties, time scales, and KPZ exponents, while exploring the connections between various classical spin systems.

Intro
Classical Spin Systems
Non Equivalent Dynamics
Classical Heisenberg Chain
Model Introduction
Dynamics
Hybrid Names
Summary
Where does it come from
Longlived Solitons
integrable perturbation
conserved numbers of charges
classical studies
comparison
Solitons
Momentum
Moving Solids
Stationary Solids
Interpolating Hamiltonian
Single Soliton
Two Particle Solutions
Conclusion
References
Questions
Equilibrium Properties
Time Scales
Infinite Time
Ishimori to ferromagnet
Second nearest neighbor ferromagnet
KPZ exponents
Solution phase shift