Yllanes, David

Title: The low-temperature phase of Ising spin glasses: parallel-tempering simulations with sample-dependent thermalisation on the Janus computer
Author: David Yllanes
Affiliation: Universidad Complutense de Madrid, Spain
Abstract:
We have performed a large-scale equilibrium simulation of the three-dimensional Ising spin glass at low temperatures, achieving thermalisation for lattices up to L=32 at temperatures as low as T=0.64Tc. This has been possible thanks to the Janus supercomputer, a custom-built massively parallel machine designed specifically for Monte Carlo simulations, which outperforms conventional computers by several orders of magnitude (during the whole simulation campaign we performed a total of 10²⁰ spin updates, which we believe is a record). Since the energy landscape of the Ising spin glass at such low temperatures is extremely complicated, parallel tempering is employed to accelerate equilibration. In this kind of simulations one typically takes the same number of Monte Carlo steps for each sample and studies the quality of the thermalisation through the time evolution of disorder averages. However, relaxation times vary wildly (several orders of magnitude) from one sample to another, so this usual simulation strategy is suboptimal. In this talk I will show how to use the random walk in temperature space during the parallel-tempering process to assess thermalisation on a sample-by-sample basis. This is more efficient than simulating all samples for a very long time and safer, too, because it exposes thermalisation biases that can be concealed by the disorder average.
We demonstrate the relevance of equilibrium finite-size simulations to understand experimental non-equilibrium spin glasses in the thermodynamical limit by establishing a time-length dictionary. We conclude that non-equilibrium experiments performed on a time scale of one hour can be matched with equilibrium results on L=110 lattices.