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We analyse 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 thetractability of its effective model. For a `half-ramp' from ferromagnet to CP,the longitudinal and transverse magnetization scale as $\tau^{-1/3}$ and$\tau^{-2/3}$, respectively, with $1/\tau$ the ramp rate, in accord withKibble-Zurek theory. For ferro- to paramagnetic ramps across the CP, however,they stay closer, $\tau^{-1/2}$ and $\tau^{-1}$, to adiabaticity. Thisadiabaticity enhancement compared to the half ramp is understood by casting thedynamics in the paramagnet in the form of a non-hermitian Dirac Hamiltonian,with the CP playing the role of an exceptional point, opening an additionaldecay channel.

Adiabaticity enhancement in the classical transverse field Ising chain, and its effective non-Hermitian description