34,493 research outputs found
: an alternative phenomenological coupling parameter for model systems
We introduce a parameter which like the kurtosis (Binder cumulant) is a
phenomenological coupling characteristic of the shape of the distribution
of the order parameter . To demonstrate the use of the parameter we
analyze extensive numerical data obtained from density of states measurements
on the canonical simple cubic spin- Ising ferromagnet, for sizes to
. Using the -parameter accurate estimates are obtained for the
critical inverse temperature , and for the thermal
exponent . In this system at least, corrections to finite size
scaling are significantly weaker for the -parameter than for the Binder
cumulant.Comment: 6 pages, 7 figures
The bimodal Ising spin glass in dimension two : the anomalous dimension
Direct measurements of the spin glass correlation function for
Gaussian and bimodal Ising spin glasses in dimension two have been carried out
in the temperature region . In the Gaussian case the data are
consistent with the known anomalous dimension value . For the
bimodal spin glass in this temperature region , well above the
crossover to the ground state dominated regime, the effective
exponent is clearly non-zero and the data are consistent with the
estimate given by McMillan in 1983 from similar
measurements. Measurements of the temperature dependence of the Binder cumulant
and the normalized correlation length for the two
models confirms the conclusion that the 2D bimodal model has a non-zero
effective both below and above . The 2D bimodal and Gaussian
interaction distribution Ising spin glasses are not in the same Universality
class.Comment: 6 pages, 8 figure
Link overlaps at Criticality and Universality in Ising Spin Glasses
Extensive simulations are made of link and spin overlaps in four and five
dimensional Ising Spin Glasses (ISGs). Moments and moment ratios of the mean
link overlap distributions (the variance, the kurtosis and the skewness) show
clear critical behavior around the ISG ordering temperature. The link overlap
measurements can be used to identify the ISG transition accurately; the link
overlap is often a more efficient tool in this context than the spin overlap
because the link overlap inter-sample variability is much weaker. Once the
transition temperature is accurately established, critical exponents can be
readily estimated by extrapolating measurements made in the thermodynamic limit
regime. The data show that the bimodal and Gaussian spin glass susceptibility
exponents are different from each other, both in dimension 5 and in
dimension 4. Hence ISG critical exponents are not universal in a given
dimension, but depend on the form of the interaction distribution.Comment: 16 pages, 30 figure
The Ising Spin Glass in dimension four
The critical behaviors of the bimodal and Gaussian Ising spin glass (ISG)
models in dimension four are studied through extensive numerical simulations,
and from an analysis of high temperature series expansion (HTSE) data of Klein
{\it et al.} (1991). The simulations include standard finite size scaling
measurements, thermodynamic limit regime measurements, and analyses which
provide estimates of critical exponents without any consideration of the
critical temperature. The higher order HTSE series for the bimodal model
provide accurate estimates of the critical temperature and critical exponents.
These estimates are independent of and fully consistent with the simulation
values. Comparisons between ISG models in dimension four show that the critical
exponents and the critical constants for dimensionless observables depend on
the form of the interaction distribution of the model.Comment: 10 pages, 15 figure
Ising Spin Glasses and Renormalization Group Theory: the Binder cumulant
Numerical data on scaling of the normalized Binder cumulant and the
normalized correlation length are shown for the Thermodynamic limit regime,
first for canonical Ising ferromagnet models and then for a range of Ising spin
glass models. A fundamental Renormalization Group Theory rule linking the
critical exponents for the two observables is well obeyed in the Ising models,
but not for the Ising spin glasses in dimensions three and four. We conclude
that there is a violation of a standard Josephson hyperscaling rule in Ising
spin glasses.Comment: 7 pages, 11 figure
Non-self-averaging in Ising spin glasses; hyperuniversality
Ising spin glasses with bimodal and Gaussian near-neighbor interaction
distributions are studied through numerical simulations. The non-self-averaging
(normalized inter-sample variance) parameter for the spin glass
susceptibility (and for higher moments ) is reported for
dimensions 2, 3, 4, 5 and 7. In each dimension the non-self-averaging
parameters in the paramagnetic regime vary with the sample size L and the
correlation length as , and
so follow a renormalization group law due to Aharony and Harris (1991).
Empirically, it is found that the values are independent of d to within
the statistics. The maximum values are almost
independent of L in each dimension, and remarkably the estimated thermodynamic
limit critical peak values are also
dimension-independent to within the statistics and so are "hyperuniversal".
These results show that the form of the spin-spin correlation function
distribution at criticality in the large limit is independent of dimension
within the ISG family. Inspection of published non-self-averaging data for 3D
Heisenberg and XY spin glasses the light of the Ising spin glass
non-self-averaging results show behavior incompatible with a spin-driven
ordering scenario, but compatible with that expected on a chiral-driven
ordering interpretation.Comment: 10 pages, 22 figure
Hyperscaling breakdown and Ising Spin Glasses: the Binder cumulant
Among the Renormalization Group Theory scaling rules relating critical
exponents, there are hyperscaling rules involving the dimension of the system.
It is well known that in Ising models hyperscaling breaks down above the upper
critical dimension. It was shown by M. Schwartz [Europhys. Lett. {\bf 15}, 777
(1991)] that the standard Josephson hyperscaling rule can also break down in
Ising systems with quenched random interactions. A related Renormalization
Group Theory hyperscaling rule links the critical exponents for the normalized
Binder cumulant and the correlation length in the thermodynamic limit. An
appropriate scaling approach for analyzing measurements from criticality to
infinite temperature is first outlined. Numerical data on the scaling of the
normalized correlation length and the normalized Binder cumulant are shown for
the canonical Ising ferromagnet model in dimension three where hyperscaling
holds, for the Ising ferromagnet in dimension five (so above the upper critical
dimension) where hyperscaling breaks down, and then for Ising spin glass models
in dimension three where the quenched interactions are random. For the Ising
spin glasses there is a breakdown of the normalized Binder cumulant
hyperscaling relation in the thermodynamic limit regime, with a return to size
independent Binder cumulant values in the finite-size scaling regime around the
critical region.Comment: 11 pages, 22 figure
Critical exponents of the binomial Ising Spin Glass in dimension four; non-universality
Extensive simulations are made on the bimodal Ising Spin Glass (ISG) in
dimension four. The transition temperature is established using a combination
of standard finite size scaling and of thermodynamic derivative peak data.
Measurements in the thermodynamic limit regime are analysed so as to estimate
critical exponents and confluent correction terms. Comparisons with results on
other 4d ISGs show that the susceptibility and correlation length critical
exponents and depend on the form of the interaction
distribution. From this observation it can be deduced that critical exponents
are not universal in ISGs.Comment: 5 pages, 5 figures. arXiv admin note: text overlap with
arXiv:1307.524
The Ising ferromagnet in dimension five: link and spin overlaps
In the simple [hyper]cubic five dimension near neighbor interaction Ising
ferromagnet, extensive simulation measurements are made of the link overlap and
the spin overlap distributions. These "two replica" measurements are standard
in the Spin Glass context but are not usually recorded in ferromagnet
simulations. The moments and moment ratios of these distributions (the
variance, the kurtosis and the skewness) show clear critical behaviors at the
known ordering temperature of the ferromagnet. Analogous overlap effects can be
expected quite generally in Ising ferromagnets in any dimension. The link
overlap results in particular, with peaks at criticality in the kurtosis and
the skewness, also have implications for Spin Glasses.Comment: 5 pages, 8 figure
Critical exponents in Ising Spin Glasses
Extensive simulations are made of the spin glass susceptibility and
correlation length in five dimension Ising Spin Glasses (ISGs) with Gaussian
and bimodal interaction distributions. Once the transition temperature is
accurately established using a standard criterion, critical exponents and
correction terms can be readily estimated by extrapolating measurements made in
the thermodynamic limit regime. The data show that the critical exponents of
the susceptibility and of the correlation length depend on the
form of the interaction distribution. This observation implies that quite
generally critical exponents are not universal in ISGs.Comment: 4 pages, 5 figure
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