3 research outputs found
Strong universality and algebraic scaling in two-dimensional Ising spin glasses
At zero temperature, two-dimensional Ising spin glasses are known to fall
into several universality classes. Here we consider the scaling at low but
non-zero temperature and provide numerical evidence that and
in all cases, suggesting a unique universality class. This
algebraic (as opposed to exponential) scaling holds in particular for the model, with or without dilutions and for the plaquette diluted model. Such a
picture, associated with an exceptional behavior at T=0, is consistent with a
real space renormalization group approach. We also explain how the scaling of
the specific heat is compatible with the hyperscaling prediction
Finite size scaling in Villain's fully frustrated model and singular effects of plaquette disorder
The ground state and low T behavior of two-dimensional spin systems with
discrete binary couplings are subtle but can be analyzed using exact
computations of finite volume partition functions. We first apply this approach
to Villain's fully frustrated model, unveiling an unexpected finite size
scaling law. Then we show that the introduction of even a small amount of
disorder on the plaquettes dramatically changes the scaling laws associated
with the T=0 critical point.Comment: Latex with 3 ps figures. Last versio
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