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Testing statics-dynamics equivalence at the spin-glass transition in three dimensions

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http://dx.doi.org/10.1103/PhysRevB.91.174202
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2015-05-26
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American Physical Society
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The statics-dynamics correspondence in spin glasses relate nonequilibrium results on large samples (the experimental realm) with equilibrium quantities computed on small systems (the typical arena for theoretical computations). Here we employ statics-dynamics equivalence to study the Ising spin-glass critical behavior in three dimensions. By means of Monte Carlo simulation, we follow the growth of the coherence length (the size of the glassy domains), on lattices too large to be thermalized. Thanks to the large coherence lengths we reach, we are able to obtain accurate results in excellent agreement with the best available equilibrium computations. To do so, we need to clarify the several physical meanings of the dynamic exponent close to the critical temperature.
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©2015 American Physical Society.We thank Enzo Marinari, Giorgio Parisi, and Andrea Maiorano for helping us with our first Pthreads programs. We also thank Andrea Pelissetto, Giorgio Parisi, and Matteo Lulli for discussing with us, prior to publication, their very interesting and accurate finite-time, finite-size scaling approach [62]. We thank as well Juan Jesus Ruiz-Lorenzo, Peter Young, and David Yllanes for discussions. The total simulation time devoted to this project was the equivalent of 36 days of the full (3072 AMD cores) Memento cluster (see http://bifi.es). We were partly supported by MINECO (Spain) through research Contract No. FIS2012-35719-C02.
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https://hdl.handle.net/20.500.14352/24126
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