87 research outputs found
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
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 ). 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
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
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