Kovacs effect in the one-dimensional Ising model: A linear response analysis

2014/01/19 by Miguel Ruiz-García, M. Ruiz-García, A. Prados
Materials Science · Mathematics · Physics and Astronomy · #Exponential function #Function (biology) #Glauber #Ising model #Material Dynamics and Properties #Mathematical analysis #Mathematics #Monotonic function #Monte Carlo method #Physics #Position (finance) #Quantum mechanics #Relaxation (psychology) #Spectroscopy and Quantum Chemical Studies #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.89.012140

published as Phys. Rev. E 89, 012140 (2014) · accepted for publication in Phys. Rev. E

arxiv created 2014/01/19 · openalex publication_date 2014/01/27 · arxiv updated 2016/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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.

Citations

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