1,740 research outputs found
Numerical simulations of Ising spin glasses with free boundary conditions: the role of droplet excitations and domain walls
The relative importance of the contributions of droplet excitations and
domain walls on the ordering of short-range Edwards-Anderson spin glasses in
three and four dimensions is studied. We compare the overlap distributions of
periodic and free boundary conditions using population annealing Monte Carlo.
For system sizes up to about 1000 spins, spin glasses show non-trivial spin
overlap distributions. Periodic boundary conditions can trap diffusive domain
walls which can contribute to small spin overlaps, and the other contribution
is the existence of low-energy droplet excitations within the system. We use
free boundary conditions to minimize domain-wall effects, and show that
low-energy droplet excitations are the major contribution to small overlaps in
numerical simulations. Free boundary conditions has stronger finite-size
effects, and is likely to have the same thermodynamic limit with periodic
boundary conditions.Comment: 5 pages, 4 figure
Population annealing: Theory and application in spin glasses
Population annealing is an efficient sequential Monte Carlo algorithm for
simulating equilibrium states of systems with rough free energy landscapes. The
theory of population annealing is presented, and systematic and statistical
errors are discussed. The behavior of the algorithm is studied in the context
of large-scale simulations of the three-dimensional Ising spin glass and the
performance of the algorithm is compared to parallel tempering. It is found
that the two algorithms are similar in efficiency though with different
strengths and weaknesses.Comment: 16 pages, 10 figures, 4 table
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