2,418 research outputs found
Scaling above the upper critical dimension in Ising Models
We rederive the finite size scaling formula for the apparent critical
temperature by using Mean Field Theory for the Ising Model above the upper
critical dimension. We have also performed numerical simulations in five
dimensions and our numerical data are in a good agreement with the Mean Field
theoretical predictions, in particular, with the finite size exponent of the
connected susceptibility and with the value of the Binder cumulant.Comment: 9 pages and 3 figures, available at
http://chimera.roma1.infn.it/index_papers_complex.htm
Generalized off-equilibrium fluctuation-dissipation relations in random Ising systems
We show that the numerical method based on the off-equilibrium
fluctuation-dissipation relation does work and is very useful and powerful in
the study of disordered systems which show a very slow dynamics. We have
verified that it gives the right information in the known cases (diluted
ferromagnets and random field Ising model far from the critical point) and we
used it to obtain more convincing results on the frozen phase of
finite-dimensional spin glasses. Moreover we used it to study the Griffiths
phase of the diluted and the random field Ising models.Comment: 20 pages, 10 figures, uses epsfig.sty. Partially presented at
StatPhys XX in a talk by one of the authors (FRT). Added 1 reference in the
new versio
Effective and asymptotic criticality of structurally disordered magnets
Changes in magnetic critical behaviour of quenched structurally-disordered
magnets are usually exemplified in experiments and in MC simulations by diluted
systems consisting of magnetic and non-magnetic components. By our study we aim
to show, that similar effects can be observed not only for diluted magnets with
non-magnetic impurities, but may be implemented, e.g., by presence of two (and
more) chemically different magnetic components as well. To this end, we
consider a model of the structurally-disordered quenched magnet where all
lattice sites are occupied by Ising-like spins of different length . In such
random spin length Ising model the length of each spin is a random variable
governed by the distribution function . We show that this model belongs
to the universality class of the site-diluted Ising model. This proves that
both models are described by the same values of asymptotic critical exponents.
However, their effective critical behaviour differs. As a case study we
consider a quenched mixture of two different magnets, with values of elementary
magnetic moments and , and of concentration and ,
correspondingly. We apply field-theoretical renormalization group approach to
analyze the renormalization group flow for different initial conditions,
triggered by and , and to calculate effective critical exponents further
away from the fixed points of the renormalization group transformation. We show
how the effective exponents are governed by difference in properties of the
magnetic components.Comment: 17 pages, 5 figures, 1 tabl
Study of the phase transition in the 3d Ising spin glass from out of equilibrium numerical simulations
Using the decay of the out equilibrium spin-spin correlation function we
compute the equilibrium Edward-Anderson order parameter in the three
dimensional binary Ising spin glass in the spin glass phase. We have checked
that the Edward-Anderson order parameter computed from out of equilibrium
numerical simulations follows with good precision the critical law as
determined in experiments and in numerical studies at equilibrium. We have also
studied the dependence of the order parameter with the lattice size. Finally we
present a large time study of the scaling of the off-equilibrium
fluctuation-dissipation relations.Comment: 14 pages, 7 Postscript figure
Summability of the perturbative expansion for a zero-dimensional disordered spin model
We show analytically that the perturbative expansion for the free energy of
the zero dimensional (quenched) disordered Ising model is Borel-summable in a
certain range of parameters, provided that the summation is carried out in two
steps: first, in the strength of the original coupling of the Ising model and
subsequently in the variance of the quenched disorder. This result is
illustrated by some high-precision calculations of the free energy obtained by
a straightforward numerical implementation of our sequential summation method.Comment: LaTeX, 12 pages and 4 figure
Simulation of 3d Ising spin glass model using three replicas: study of Binder cumulants
We have carried out numerical simulations of the three-dimensional Ising spin
glass model with first neighbour Gaussian couplings using three replicas for
each sample of couplings. We have paid special attention to the measure of two
types of Binder cumulant that can be constructed from the three possible
overlaps between the replicas. We obtain new information about the possible
phase transition and perform an initial analysis of the ultrametricity issue.Comment: 14 pages and 7 figures, available at
http://chimera.roma1.infn.it/index_papers_complex.htm
Crossovers in the Two Dimensional Ising Spin Glass with ferromagnetic next-nearest-neighbor interactions
By means of extensive computer simulations we analyze in detail the two
dimensional Ising spin glass with ferromagnetic next-nearest-neighbor
interactions. We found a crossover from ferromagnetic to ``spin glass'' like
order both from numerical simulations and analytical arguments. We also present
evidences of a second crossover from the ``spin glass'' behavior to a
paramagnetic phase for the largest volume studied.Comment: 19 pages with 9 postscript figures also available at
http://chimera.roma1.infn.it/index_papers_complex.html. Some changes in
captions of figures 1 and
Griffiths singularities in the two dimensional diluted Ising model
We study numerically the probability distribution of the Yang-Lee zeroes
inside the Griffiths phase for the two dimensional site diluted Ising model and
we check that the shape of this distribution is that predicted in previous
analytical works. By studying the finite size scaling of the averaged smallest
zero at the phase transition we extract, for two values of the dilution, the
anomalous dimension, , which agrees very well with the previous estimated
values.Comment: 11 pages and 4 figures, some minor changes in Fig. 4, available at
http://chimera.roma1.infn.it/index_papers_complex.htm
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