We analyze the near-adiabatic dynamics in a ramp through the critical point (CP) of the classical transverse field Ising chain. This is motivated, conceptually, by the fact that this CP—unlike its quantum counterpart—experiences no thermal or quantum fluctuations, and technically by the tractability of its effective model. For a “half ramp” from a ferromagnet to the CP, the longitudinal and transverse magnetizations scale as ${\tau }^{-1/3}$ and ${\tau }^{-2/3}$, respectively, with $1/\tau$ the ramp rate, in accord with Kibble-Zurek theory. For ferro- to paramagnetic ramps across the CP, however, they stay closer, ${\tau }^{-1/2}$ and ${\tau }^{-1}$, to adiabaticity. This adiabaticity enhancement compared to the half ramp is understood by casting the dynamics in the paramagnet in the form of a non-Hermitian Dirac Hamiltonian, with the CP playing the role of an exceptional point, opening an additional decay channel.

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• Quantum quench
• Non-Hermitian systems
• Classical spin chains