3 research outputs found
Feedback-optimized parallel tempering Monte Carlo
We introduce an algorithm to systematically improve the efficiency of
parallel tempering Monte Carlo simulations by optimizing the simulated
temperature set. Our approach is closely related to a recently introduced
adaptive algorithm that optimizes the simulated statistical ensemble in
generalized broad-histogram Monte Carlo simulations. Conventionally, a
temperature set is chosen in such a way that the acceptance rates for replica
swaps between adjacent temperatures are independent of the temperature and
large enough to ensure frequent swaps. In this paper, we show that by choosing
the temperatures with a modified version of the optimized ensemble feedback
method we can minimize the round-trip times between the lowest and highest
temperatures which effectively increases the efficiency of the parallel
tempering algorithm. In particular, the density of temperatures in the
optimized temperature set increases at the "bottlenecks'' of the simulation,
such as phase transitions. In turn, the acceptance rates are now temperature
dependent in the optimized temperature ensemble. We illustrate the
feedback-optimized parallel tempering algorithm by studying the two-dimensional
Ising ferromagnet and the two-dimensional fully-frustrated Ising model, and
briefly discuss possible feedback schemes for systems that require
configurational averages, such as spin glasses.Comment: 12 pages, 14 figure
Critical behavior of the random-anisotropy model in the strong-anisotropy limit
We investigate the nature of the critical behavior of the random-anisotropy
Heisenberg model (RAM), which describes a magnetic system with random uniaxial
single-site anisotropy, such as some amorphous alloys of rare earths and
transition metals. In particular, we consider the strong-anisotropy limit
(SRAM), in which the Hamiltonian can be rewritten as the one of an Ising
spin-glass model with correlated bond disorder. We perform Monte Carlo
simulations of the SRAM on simple cubic L^3 lattices, up to L=30, measuring
correlation functions of the replica-replica overlap, which is the order
parameter at a glass transition. The corresponding results show critical
behavior and finite-size scaling. They provide evidence of a finite-temperature
continuous transition with critical exponents and
. These results are close to the corresponding estimates that
have been obtained in the usual Ising spin-glass model with uncorrelated bond
disorder, suggesting that the two models belong to the same universality class.
We also determine the leading correction-to-scaling exponent finding .Comment: 24 pages, 13 figs, J. Stat. Mech. in pres