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The Kovacs effect in the one-dimensional Ising model: a linear response analysis
We analyze the so-called Kovacs effect in the one-dimensional Ising model
with Glauber dynamics. We consider small enough temperature jumps, for which a
linear response theory has been recently derived. Within this theory, the
Kovacs hump is directly related to the monotonic relaxation function of the
energy. The analytical results are compared with extensive Monte Carlo
simulations, and an excellent agreement is found. Remarkably, the position of
the maximum in the Kovacs hump depends on the fact that the true asymptotic
behavior of the relaxation function is different from the stretched exponential
describing the relevant part of the relaxation at low temperatures.Comment: accepted for publication in Phys. Rev.
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