25 research outputs found
Non-equilibrium Relations for Spin Glasses with Gauge Symmetry
We study the applications of non-equilibrium relations such as the Jarzynski
equality and fluctuation theorem to spin glasses with gauge symmetry. It is
shown that the exponentiated free-energy difference appearing in the Jarzynski
equality reduces to a simple analytic function written explicitly in terms of
the initial and final temperatures if the temperature satisfies a certain
condition related to gauge symmetry. This result is used to derive a lower
bound on the work done during the non-equilibrium process of temperature
change. We also prove identities relating equilibrium and non-equilibrium
quantities. These identities suggest a method to evaluate equilibrium
quantities from non-equilibrium computations, which may be useful to avoid the
problem of slow relaxation in spin glasses.Comment: 8 pages, 2 figures, submitted to JPS
Testing Error Correcting Codes by Multicanonical Sampling of Rare Events
The idea of rare event sampling is applied to the estimation of the
performance of error-correcting codes. The essence of the idea is importance
sampling of the pattern of noises in the channel by Multicanonical Monte Carlo,
which enables efficient estimation of tails of the distribution of bit error
rate. The idea is successfully tested with a convolutional code
Simulation of Lattice Polymers with Multi-Self-Overlap Ensemble
A novel family of dynamical Monte Carlo algorithms for lattice polymers is
proposed. Our central idea is to simulate an extended ensemble in which the
self-avoiding condition is systematically weakened. The degree of the
self-overlap is controlled in a similar manner as the multicanonical ensemble.
As a consequence, the ensemble --the multi-self-overlap ensemble-- contains
adequate portions of self-overlapping conformations as well as higher energy
ones. It is shown that the multi-self-overlap ensemble algorithm reproduce
correctly the canonical averages at finite temperatures of the HP model of
lattice proteins. Moreover, it outperforms massively a standard multicanonical
algorithm for a difficult example of a polymer with 8-stickers. Alternative
algorithm based on exchange Monte Carlo method is also discussed.Comment: 5 Pages, 4 Postscript figures, uses epsf.st
Nonequilibrium work on spin glasses in longitudinal and transverse fields
We derive a number of exact relations between equilibrium and nonequilibrium
quantities for spin glasses in external fields using the Jarzynski equality and
gauge symmetry. For randomly-distributed longitudinal fields, a lower bound is
established for the work done on the system in nonequilibrium processes, and
identities are proven to relate equilibrium and nonequilibrium quantities. In
the case of uniform transverse fields, identities are proven between physical
quantities and exponentiated work done to the system at different parts of the
phase diagram with the context of quantum annealing in mind. Additional
relations are given, which relate the exponentiated work in quantum and
simulated (classical) annealing. It is also suggested that the Jarzynski
equality may serve as a guide to develop a method to perform quantum annealing
under non-adiabatic conditions.Comment: 17 pages, 5 figures, submitted to JPS
A List Referring Monte Carlo Method for Lattice Glass Models
We present an effcient Monte-Carlo method for lattice glass models which are
characterized by hard constraint conditions. The basic idea of the method is
similar to that of the -fold way method. By using a list of sites into which
we can insert a particle, we avoid trying a useless transition which is
forbidden by the constraint conditions. We applied the present method to a
lattice glass model proposed by Biroli and M{\'e}zard. We first evaluated the
efficiency of the method through measurements of the autocorrelation function
of particle configurations. As a result, we found that the efficiency is much
higher than that of the standard Monte-Carlo method. We also compared the
efficiency of the present method with that of the -fold way method in
detail. We next examined how the efficiency of extended ensemble methods such
as the replica exchange method and the Wang-Landau method is inflnuenced by the
choice of the local update method. The results show that the efficiency is
considerably improved by the use of efficient local update methods. For
example, when the number of sites is 1024, the ergodic time
of the replica exchange method in the grand-canonical ensemble,
which is the average round-trip time of a replica in chemical-potential space,
with the present local update method is more than times shorter than
that with the standard local update method. This result shows that the
efficient local update method is quite important to make extended ensemble
methods more effective.Comment: 16 pages, 21 figures; 1 subsection, 1 appendix, and 5 figures are
added, abstract is changed, 1 figure is remove
Equilibrium Sampling From Nonequilibrium Dynamics
We present some applications of an Interacting Particle System (IPS)
methodology to the field of Molecular Dynamics. This IPS method allows several
simulations of a switched random process to keep closer to equilibrium at each
time, thanks to a selection mechanism based on the relative virtual work
induced on the system. It is therefore an efficient improvement of usual
non-equilibrium simulations, which can be used to compute canonical averages,
free energy differences, and typical transitions paths
Large random correlations in individual mean field spin glass samples
We argue that complex systems must possess long range correlations and
illustrate this idea on the example of the mean field spin glass model. Defined
on the complete graph, this model has no genuine concept of distance, but the
long range character of correlations is translated into a broad distribution of
the spin-spin correlation coefficients for almost all realizations of the
random couplings. When we sample the whole phase space we find that this
distribution is so broad indeed that at low temperatures it essentially becomes
uniform, with all possible correlation values appearing with the same
probability. The distribution of correlations inside a single phase space
valley is also studied and found to be much narrower.Comment: Added a few references and a comment phras
Evidence for the double degeneracy of the ground-state in the 3D spin glass
A bivariate version of the multicanonical Monte Carlo method and its
application to the simulation of the three-dimensional Ising spin glass
are described. We found the autocorrelation time associated with this
particular multicanonical method was approximately proportional to the system
volume, which is a great improvement over previous methods applied to
spin-glass simulations. The principal advantage of this version of the
multicanonical method, however, was its ability to access information
predictive of low-temperature behavior. At low temperatures we found results on
the three-dimensional Ising spin glass consistent with a double
degeneracy of the ground-state: the order-parameter distribution function
converged to two delta-function peaks and the Binder parameter
approached unity as the system size was increased. With the same density of
states used to compute these properties at low temperature, we found their
behavior changing as the temperature is increased towards the spin glass
transition temperature. Just below this temperature, the behavior is consistent
with the standard mean-field picture that has an infinitely degenerate ground
state. Using the concept of zero-energy droplets, we also discuss the structure
of the ground-state degeneracy. The size distribution of the zero-energy
droplets was found to produce the two delta-function peaks of .Comment: 33 pages with 31 eps figures include
Parallel Excluded Volume Tempering for Polymer Melts
We have developed a technique to accelerate the acquisition of effectively
uncorrelated configurations for off-lattice models of dense polymer melts which
makes use of both parallel tempering and large scale Monte Carlo moves. The
method is based upon simulating a set of systems in parallel, each of which has
a slightly different repulsive core potential, such that a thermodynamic path
from full excluded volume to an ideal gas of random walks is generated. While
each system is run with standard stochastic dynamics, resulting in an NVT
ensemble, we implement the parallel tempering through stochastic swaps between
the configurations of adjacent potentials, and the large scale Monte Carlo
moves through attempted pivot and translation moves which reach a realistic
acceptance probability as the limit of the ideal gas of random walks is
approached. Compared to pure stochastic dynamics, this results in an increased
efficiency even for a system of chains as short as monomers, however
at this chain length the large scale Monte Carlo moves were ineffective. For
even longer chains the speedup becomes substantial, as observed from
preliminary data for
Enhanced and effective conformational sampling of protein molecular systems for their free energy landscapes
Protein folding and protein–ligand docking have long persisted as important subjects in biophysics. Using multicanonical molecular dynamics (McMD) simulations with realistic expressions, i.e., all-atom protein models and an explicit solvent, free-energy landscapes have been computed for several systems, such as the folding of peptides/proteins composed of a few amino acids up to nearly 60 amino-acid residues, protein–ligand interactions, and coupled folding and binding of intrinsically disordered proteins. Recent progress in conformational sampling and its applications to biophysical systems are reviewed in this report, including descriptions of several outstanding studies. In addition, an algorithm and detailed procedures used for multicanonical sampling are presented along with the methodology of adaptive umbrella sampling. Both methods control the simulation so that low-probability regions along a reaction coordinate are sampled frequently. The reaction coordinate is the potential energy for multicanonical sampling and is a structural identifier for adaptive umbrella sampling. One might imagine that this probability control invariably enhances conformational transitions among distinct stable states, but this study examines the enhanced conformational sampling of a simple system and shows that reasonably well-controlled sampling slows the transitions. This slowing is induced by a rapid change of entropy along the reaction coordinate. We then provide a recipe to speed up the sampling by loosening the rapid change of entropy. Finally, we report all-atom McMD simulation results of various biophysical systems in an explicit solvent