6 research outputs found
The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states
The nature of the zero temperature ordering transition in the 3D Gaussian
random field Ising magnet is studied numerically, aided by scaling analyses. In
the ferromagnetic phase the scaling of the roughness of the domain walls,
, is consistent with the theoretical prediction .
As the randomness is increased through the transition, the probability
distribution of the interfacial tension of domain walls scales as for a single
second order transition. At the critical point, the fractal dimensions of
domain walls and the fractal dimension of the outer surface of spin clusters
are investigated: there are at least two distinct physically important fractal
dimensions. These dimensions are argued to be related to combinations of the
energy scaling exponent, , which determines the violation of
hyperscaling, the correlation length exponent , and the magnetization
exponent . The value is derived from the
magnetization: this estimate is supported by the study of the spin cluster size
distribution at criticality. The variation of configurations in the interior of
a sample with boundary conditions is consistent with the hypothesis that there
is a single transition separating the disordered phase with one ground state
from the ordered phase with two ground states. The array of results are shown
to be consistent with a scaling picture and a geometric description of the
influence of boundary conditions on the spins. The details of the algorithm
used and its implementation are also described.Comment: 32 pp., 2 columns, 32 figure
Isotopic Grand Unification with the Inclusion of Gravity (revised version)
We introduce a dual lifting of unified gauge theories, the first
characterized by the isotopies, which are axiom- preserving maps into broader
structures with positive-definite generalized units used for the representation
of matter under the isotopies of the Poincare' symmetry, and the second
characterized by the isodualities, which are anti-isomorphic maps with
negative-definite generalized units used for the representation of antimatter
under the isodualities of the Poincare' symmetry. We then submit, apparently
for the first time, a novel grand unification with the inclusion of gravity for
matter embedded in the generalized positive-definite units of unified gauge
theories while gravity for antimatter is embedded in the isodual isounit. We
then show that the proposed grand unification provides realistic possibilities
for a resolution of the axiomatic incompatibilities between gravitation and
electroweak interactions due to curvature, antimatter and the fundamental
space-time symmetries.Comment: 20 pages, Latex, revised in various details and with added reference
Critical aspects of the random-field Ising model
We investigate the critical behavior of the three-dimensional random-field Ising model
(RFIM) with a Gaussian field distribution at zero temperature. By implementing a
computational approach that maps the ground-state of the RFIM to the maximum-flow
optimization problem of a network, we simulate large ensembles of disorder realizations of
the model for a broad range of values of the disorder strength h and
system sizes  = L3, with L â€Â 156. Our averaging procedure
outcomes previous studies of the model, increasing the sampling of ground states by a
factor of 103. Using well-established finite-size scaling schemes, the
fourth-orderâs Binder cumulant, and the sample-to-sample fluctuations of various
thermodynamic quantities, we provide high-accuracy estimates for the critical field
hc, as well as the critical exponents Μ,
ÎČ/Îœ, and ÎłÌ
/Μ of the correlation length, order parameter, and
disconnected susceptibility, respectively. Moreover, using properly defined noise to
signal ratios, we depict the variation of the self-averaging property of the model, by
crossing the phase boundary into the ordered phase. Finally, we discuss the controversial
issue of the specific heat based on a scaling analysis of the bond energy, providing
evidence that its critical exponent α â 0â
Universality aspects of the trimodal random-field Ising model
We investigate the critical properties of the d = 3 random-field Ising
model with an equal-weight trimodal distribution at zero temperature. By implementing
suitable graph-theoretical algorithms, we compute large ensembles of ground states for
several values of the disorder strength h and system sizes up to
NÂ =Â 1283. Using a new approach based on the sample-to-sample
fluctuations of the order parameter of the system and proper finite-size scaling
techniques we estimate the critical disorder strength
hc = 2.747(3) and the critical exponents of the correlation
length Μ = 1.34(6) and order parameter ÎČ = 0.016(4).
These estimates place the model into the universality class of the corresponding Gaussian
random-field Ising model