Numerical study of barriers and valleys in the free-energy landscape of spin glasses

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We study the problem of glassy relaxations in the presence of an external field in the highly controlled context of a spin-glass simulation. We consider a small spin glass in three dimensions (specifically, a lattice of size L = 8, small enough to be equilibrated through a parallel tempering simulations at low temperatures, deep in the spin glass phase). After equilibrating the sample, an external field is switched on, and the subsequent dynamics is studied. The field turns out to reduce the relaxation time, but huge statistical fluctuations are found when different samples are compared. After taking care of these fluctuations we find that the expected linear regime is very narrow. Nevertheless, when regarded as a purely numerical method, we find that the external field is extremely effective in reducing the relaxation times.
©2019 IOP Publishing We thank E Marinari, D Yllanes and F Ladieu for encouraging discussions. This work was partially supported by Ministerio de Economia, Industria y Competitividad (MINECO) Grants No. FIS2015-65078-C2, No. FIS2016-76359-P (both partly funded by FEDER). We were also partly funded by the Junta de Extremadura (Spain) through Grants No. GRU10158 and IB1603 (partially funded by FEDER). This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant No. 694925 GlassUniversality).
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