511 research outputs found
A challenge for critical point of spin glass in ground state
We show several calculations to identify the critical point in the ground
state in random spin systems including spin glasses on the basis of the duality
analysis. The duality analysis is a profound method to obtain the precise
location of the critical point in finite temperature even for spin glasses. We
propose a single equality for identifying the critical point in the ground
state from several speculations. The equality can indeed give the exact
location of the critical points for the bond-dilution Ising model on several
lattices and provides insight on further analysis on the ground state in spin
glasses.Comment: 7 pages, 2 figures, to appear in Proceedings of 4th YSM-SPIP (Sendai,
14-16 December 2012
Langevin dynamics neglecting detailed balance condition
An improved method for driving a system into a desired distribution, for
example, the Gibbs-Boltzmann distribution, is proposed, which makes use of an
artificial relaxation process. The standard techniques for achieving the
Gibbs-Boltzmann distribution involve numerical simulations under the detailed
balance condition. In contrast, in the present study we formulate the Langevin
dynamics, for which the corresponding Fokker-Planck operator includes an
asymmetric component violating the detailed balance condition. This leads to
shifts in the eigenvalues and results in the acceleration of the relaxation
toward the steady state. The numerical implementation demonstrates faster
convergence and shorter correlation time, and the technique of biased event
sampling, Nemoto-Sasa theory, further highlights the efficacy of our method.Comment: 5 pages, published in PRE (The previous title was "Acceleration of
Monte Carlo simulations without detailed balance condition from Perspective
of Nonequilibrium Behavior"
Mathematical understanding of detailed balance condition violation and its application to Langevin dynamics
We develop an efficient sampling method by simulating Langevin dynamics with
an artificial force rather than a natural force by using the gradient of the
potential energy. The standard technique for sampling following the
predetermined distribution such as the Gibbs-Boltzmann one is performed under
the detailed balance condition. In the present study, we propose a modified
Langevin dynamics violating the detailed balance condition on the
transition-probability formulation. We confirm that the numerical
implementation of the proposed method actually demonstrates two major
beneficial improvements: acceleration of the relaxation to the predetermined
distribution and reduction of the correlation time between two different
realizations in the steady state.Comment: 18pages, 3 figures, proceeedings of STATPHYS KOLKATA VII
Multicritical point of spin glasses
We present a theoretical framework to accurately calculate the location of
the multicritical point in the phase diagram of spin glasses. The result shows
excellent agreement with numerical estimates. The basic idea is a combination
of the duality relation, the replica method, and the gauge symmetry. An
additional element of the renormalization group, in particular in the context
of hierarchical lattices, leads to impressive improvements of the predictions.Comment: 6 pages, 3 figures, Dedicated to Prof. A. Nihat Berker on the
occasion of his sixtieth birthday. to appear in Physica
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