Rugged free-energy landscapes in disordered spin systems

This thesis is an attempt to provide a new outlook on complex systems, as well as some physical answers for certain models, taking a computational approach. We have focused on disordered systems, addressing two traditional problems in three spatial dimensions: the Edwards-Anderson spin glass and the Diluted Antiferromagnet in a Field (the physical realisation of the random-field Ising model). These systems have been studied by means of large-scale Monte Carlo simulations, exploiting a variety of platforms, which include the Janus special-purpose supercomputer. Two main themes are explored throughout: a) the relationship between the (experimentally unreachable) equilibrium phase and the non-equilibrium evolution and b) the computation and efficient treatment of rugged free-energy landscapes. We perform a thorough study of the low-temperature phase of the D=3 Edwards-Anderson spin glass, where we establish a time-length dictionary and a finite-time scaling formalism to link, in a quantitative way, the experimental non-equilibrium regime and the finite-size equilibrium phase. At the experimentally relevant scales, the replica symmetry breaking theory emerges as the appropriate theoretical picture. We also introduce Tethered Monte Carlo, a general strategy for the study of systems with rugged free-energy landscapes. This formalism provides a general method to guide the exploration of the configuration space by constraining one or more reaction coordinates. From these tethered simulations, the Helmholtz potential associated to the reaction coordinates is reconstructed, yielding all the information about the system. We use this method to provide a comprehensive picture of the critical behaviour in the Diluted Antiferromagnet in a Field.Comment: PhD Thesis. Defended at the Universidad Complutense de Madrid on October 21, 201

Explicit generation of the branching tree of states in spin glasses

We present a numerical method to generate explicit realizations of the tree of states in mean-field spin glasses. The resulting study illuminates the physical meaning of the full replica symmetry breaking solution and provides detailed information on the structure of the spin-glass phase. A cavity approach ensures that the method is self-consistent and permits the evaluation of sophisticated observables, such as correlation functions. We include an example application to the study of finite-size effects in single-sample overlap probability distributions, a topic that has attracted considerable interest recently.Comment: Version accepted for publication in JSTA

Temperature chaos is a non-local effect

Temperature chaos plays a role in important effects, like for example memory and rejuvenation, in spin glasses, colloids, polymers. We numerically investigate temperature chaos in spin glasses, exploiting its recent characterization as a rare-event driven phenomenon. The peculiarities of the transformation from periodic to anti-periodic boundary conditions in spin glasses allow us to conclude that temperature chaos is non-local: no bounded region of the system causes it. We precise the statistical relationship between temperature chaos and the free-energy changes upon varying boundary conditions.Comment: 15 pages, 8 figures. Version accepted for publication in JSTA

The cumulative overlap distribution function in realistic spin glasses

We use a sample-dependent analysis, based on medians and quantiles, to analyze the behavior of the overlap probability distribution of the Sherrington-Kirkpatrick and 3D Edwards-Anderson models of Ising spin glasses. We find that this approach is an effective tool to distinguish between RSB-like and droplet-like behavior of the spin-glass phase. Our results are in agreement with a RSB-like behavior for the 3D Edwards-Anderson model.Comment: Version accepted in PRB. 12 pages, 10 figure

Comprehensive study of the critical behavior in the diluted antiferromagnet in a field

We study the critical behavior of the Diluted Antiferromagnet in a Field with the Tethered Monte Carlo formalism. We compute the critical exponents (including the elusive hyperscaling violations exponent $\theta$). Our results provide a comprehensive description of the phase transition and clarify the inconsistencies between previous experimental and theoretical work. To do so, our method addresses the usual problems of numerical work (large tunneling barriers and self-averaging violations).Comment: 4 pages, 2 figure