Slow Cooling of an Ising Ferromagnet

Abstract

A ferromagnetic Ising chain which is endowed with a single-spin-flip Glauber dynamics is investigated. For an arbitrary annealing protocol, we derive an exact integral equation for the domain wall density. This integral equation admits an asymptotic solution in the limit of extremely slow cooling. For instance, we extract an asymptotic of the density of domain walls at the end of the cooling procedure when the temperature vanishes. Slow annealing is usually studied using a Kibble-Zurek argument; in our setting, this argument leads to approximate predictions which are in good agreement with exact asymptotics.

6 pages

References in corpus (3)

• Universal adiabatic dynamics across a quantum critical point
• Freezing into Stripe States in Two-Dimensional Ferromagnets and Crossing Probabilities in Critical Percolation
• Cooling dynamics of pure and random Ising chains

Cited by in corpus (14)

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• Quantum Kibble-Zurek mechanism: Kink correlations after a quench in the quantum Ising chain
• Dynamic scaling of topological ordering in classical systems
• Dynamical symmetry breaking with optimal control: reducing the number of pieces
• Slow quench dynamics in classical systems: kinetic Ising model and zero-range process
• Quantum Vertex Model for Reversible Classical Computing
• The Glauber-Ising chain under low-temperature protocols
• Universal Critical Holography and Domain Wall Formation
• Annealing Dynamics of Regular Rotor Networks: Universality and Its Breakdown
• Nonequilibrium generation of charge defects in kagome spin ice under slow cooling