139 research outputs found
Monte-Carlo study of scaling exponents of rough surfaces and correlated percolation
We calculate the scaling exponents of the two-dimensional correlated
percolation cluster's hull and unscreened perimeter. Correlations are
introduced through an underlying correlated random potential, which is used to
define the state of bonds of a two-dimensional bond percolation model.
Monte-Carlo simulations are run and the values of the scaling exponents are
determined as functions of the Hurst exponent H in the range -0.75 <= H <= 1.
The results confirm the conjectures of earlier studies
Metal-superconductor transition at zero temperature: A case of unusual scaling
An effective field theory is derived for the normal metal-to-superconductor
quantum phase transition at T=0. The critical behavior is determined exactly
for all dimensions d>2. Although the critical exponents \beta and \nu do not
exist, the usual scaling relations, properly reinterpreted, still hold. A
complete scaling description of the transition is given, and the physics
underlying the unusual critical behavior is discussed. Quenched disorder leads
to anomalously strong T_c-fluctuations which are shown to explain the
experimentally observed broadening of the transition in low-T_c thin films.Comment: 4 pp., no figs, final version as publishe
Explicit Renormalization Group for D=2 random bond Ising model with long-range correlated disorder
We investigate the explicit renormalization group for fermionic field
theoretic representation of two-dimensional random bond Ising model with
long-range correlated disorder. We show that a new fixed point appears by
introducing a long-range correlated disorder. Such as the one has been observed
in previous works for the bosonic () description. We have calculated
the correlation length exponent and the anomalous scaling dimension of
fermionic fields at this fixed point. Our results are in agreement with the
extended Harris criterion derived by Weinrib and Halperin.Comment: 5 page
Study of Percolative Transitions with First-Order Characteristics in the Context of CMR Manganites
The unusual magneto-transport properties of manganites are widely believed to
be caused by mixed-phase tendencies and concomitant percolative processes.
However, dramatic deviations from "standard" percolation have been unveiled
experimentally. Here, a semi-phenomenological description of Mn oxides is
proposed based on coexisting clusters with smooth surfaces, as suggested by
Monte Carlo simulations of realistic models for manganites, also briefly
discussed here. The present approach produces fairly abrupt percolative
transitions and even first-order discontinuities, in agreement with
experiments. These transitions may describe the percolation that occurs after
magnetic fields align the randomly oriented ferromagnetic clusters believed to
exist above the Curie temperature in Mn oxides. In this respect, part of the
manganite phenomenology could belong to a new class of percolative processes
triggered by phase competition and correlations.Comment: 4 pages, 4 eps figure
Random quantum magnets with long-range correlated disorder: Enhancement of critical and Griffiths-McCoy singularities
We study the effect of spatial correlations in the quenched disorder on
random quantum magnets at and near a quantum critical point. In the random
transverse field Ising systems disorder correlations that decay algebraically
with an exponent rho change the universality class of the transition for small
enough rho and the off-critical Griffiths-McCoy singularities are enhanced. We
present exact results for 1d utilizing a mapping to fractional Brownian motion
and generalize the predictions for the critical exponents and the generalized
dynamical exponent in the Griffiths phase to d>=2.Comment: 4 pages RevTeX, 1 eps-figure include
Susceptibility and Percolation in 2D Random Field Ising Magnets
The ground state structure of the two-dimensional random field Ising magnet
is studied using exact numerical calculations. First we show that the
ferromagnetism, which exists for small system sizes, vanishes with a large
excitation at a random field strength dependent length scale. This {\it
break-up length scale} scales exponentially with the squared random
field, . By adding an external field we then study the
susceptibility in the ground state. If , domains melt continuously and
the magnetization has a smooth behavior, independent of system size, and the
susceptibility decays as . We define a random field strength dependent
critical external field value , for the up and down spins to
form a percolation type of spanning cluster. The percolation transition is in
the standard short-range correlated percolation universality class. The mass of
the spanning cluster increases with decreasing and the critical
external field approaches zero for vanishing random field strength, implying
the critical field scaling (for Gaussian disorder) , where and .
Below the systems should percolate even when H=0. This implies that
even for H=0 above the domains can be fractal at low random fields, such
that the largest domain spans the system at low random field strength values
and its mass has the fractal dimension of standard percolation .
The structure of the spanning clusters is studied by defining {\it red
clusters}, in analogy to the ``red sites'' of ordinary site-percolation. The
size of red clusters defines an extra length scale, independent of .Comment: 17 pages, 28 figures, accepted for publication in Phys. Rev.
Random Walks with Long-Range Self-Repulsion on Proper Time
We introduce a model of self-repelling random walks where the short-range
interaction between two elements of the chain decreases as a power of the
difference in proper time. Analytic results on the exponent are obtained.
They are in good agreement with Monte Carlo simulations in two dimensions. A
numerical study of the scaling functions and of the efficiency of the algorithm
is also presented.Comment: 25 pages latex, 4 postscript figures, uses epsf.sty (all included)
IFUP-Th 13/92 and SNS 14/9
Site-diluted three dimensional Ising Model with long-range correlated disorder
We study two different versions of the site-diluted Ising model in three
dimensions with long-range spatially correlated disorder by Monte Carlo means.
We use finite-size scaling techniques to compute the critical exponents of
these systems, taking into account the strong scaling-corrections. We find a
value that is compatible with the analytical predictions.Comment: 19 pages, 1 postscript figur
Percolation in three-dimensional random field Ising magnets
The structure of the three-dimensional random field Ising magnet is studied
by ground state calculations. We investigate the percolation of the minority
spin orientation in the paramagnetic phase above the bulk phase transition,
located at [Delta/J]_c ~= 2.27, where Delta is the standard deviation of the
Gaussian random fields (J=1). With an external field H there is a disorder
strength dependent critical field +/- H_c(Delta) for the down (or up) spin
spanning. The percolation transition is in the standard percolation
universality class. H_c ~ (Delta - Delta_p)^{delta}, where Delta_p = 2.43 +/-
0.01 and delta = 1.31 +/- 0.03, implying a critical line for Delta_c < Delta <=
Delta_p. When, with zero external field, Delta is decreased from a large value
there is a transition from the simultaneous up and down spin spanning, with
probability Pi_{uparrow downarrow} = 1.00 to Pi_{uparrow downarrow} = 0. This
is located at Delta = 2.32 +/- 0.01, i.e., above Delta_c. The spanning cluster
has the fractal dimension of standard percolation D_f = 2.53 at H = H_c(Delta).
We provide evidence that this is asymptotically true even at H=0 for Delta_c <
Delta <= Delta_p beyond a crossover scale that diverges as Delta_c is
approached from above. Percolation implies extra finite size effects in the
ground states of the 3D RFIM.Comment: replaced with version to appear in Physical Review
Percolation in random environment
We consider bond percolation on the square lattice with perfectly correlated
random probabilities. According to scaling considerations, mapping to a random
walk problem and the results of Monte Carlo simulations the critical behavior
of the system with varying degree of disorder is governed by new, random fixed
points with anisotropic scaling properties. For weaker disorder both the
magnetization and the anisotropy exponents are non-universal, whereas for
strong enough disorder the system scales into an {\it infinite randomness fixed
point} in which the critical exponents are exactly known.Comment: 8 pages, 7 figure
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