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1.
N. G. Fytas A. Malakis 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,50(1-2):39-43
The three-dimensional bimodal random-field Ising model is studied
via a new finite temperature numerical approach. The methods of
Wang-Landau sampling and broad histogram are implemented in a
unified algorithm by using the N-fold version of the Wang-Landau
algorithm. The simulations are performed in dominant energy
subspaces, determined by the recently developed critical minimum
energy subspace technique. The random-fields are obtained from a
bimodal distribution, that is we consider the discrete
(±Δ) case and the model is studied on cubic lattices with
sizes 4≤L ≤20. In order to extract information for the
relevant probability distributions of the specific heat and
susceptibility peaks, large samples of random-field realizations
are generated. The general aspects of the model's scaling behavior
are discussed and the process of averaging finite-size anomalies
in random systems is re-examined under the prism of the lack of
self-averaging of the specific heat and susceptibility of the
model. 相似文献
2.
A.K. Hartmann U. Nowak 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,7(1):105-109
We investigate the critical behavior of three-dimensional random-field Ising systems with both Gauss and bimodal distribution
of random fields and additional the three-dimensional diluted Ising antiferromagnet in an external field. These models are
expected to be in the same universality class. We use exact ground-state calculations with an integer optimization algorithm
and by a finite-size scaling analysis we calculate the critical exponents , , and . While the random-field model with Gauss distribution of random fields and the diluted antiferromagnet appear to be in same
universality class, the critical exponents of the random-field model with bimodal distribution of random fields seem to be
significantly different.
Received: 9 July 1998 / Received in final form: 15 July 1998 / Accepted: 20 July
1998 相似文献
3.
N. G. Fytas A. Malakis 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,61(1):111-120
The one-parametric Wang-Landau (WL) method is
implemented together with an extrapolation scheme to yield
approximations of the two-dimensional (exchange-energy,
field-energy) density of states (DOS) of the 3D bimodal
random-field Ising model (RFIM). The present approach generalizes
our earlier WL implementations, by handling the final stage of the
WL process as an entropic sampling scheme, appropriate for the
recording of the required two-parametric histograms. We test the
accuracy of the proposed extrapolation scheme and then apply it to
study the size-shift behavior of the phase diagram of the 3D
bimodal RFIM. We present a finite-size converging approach and a
well-behaved sequence of estimates for the critical disorder
strength. Their asymptotic shift-behavior yields the critical
disorder strength and the associated correlation length's
exponent, in agreement with previous estimates from ground-state
studies of the model. 相似文献
4.
5.
R. Mélin K. Biljaković J.C. Lasjaunias P. Monceau 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,26(4):417-430
We show that the dynamics of disordered charge density waves (CDWs) and spin density waves (SDWs) is a collective phenomenon.
The very low temperature specific heat relaxation experiments are characterized by: (i) “interrupted” ageing (meaning that
there is a maximal relaxation time); and (ii) a broad power-law spectrum of relaxation times which is the signature of a collective
phenomenon. We propose a random energy model that can reproduce these two observations and from which it is possible to obtain
an estimate of the glass cross-over temperature (typically T
g≃ 100-200 mK). The broad relaxation time spectrum can also be obtained from the solutions of two microscopic models involving
randomly distributed solitons. The collective behavior is similar to domain growth dynamics in the presence of disorder and
can be described by the dynamical renormalization group that was proposed recently for the one dimensional random field Ising
model [D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80, 3539 (1998)]. The typical relaxation time scales like ∼τexp(T
g/T). The glass cross-over temperature Tg related to correlations among solitons is equal to the average energy barrier and scales like T
g∼ 2xξΔ. x is the concentration of defects, ξ the correlation length of the CDW or SDW and Δ the charge or spin gap.
Received 12 December 2001 相似文献
6.
G.L.S. Paula W. Figueiredo 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,1(4):519-522
The stationary states of the random-field Ising model are determined through the master equation approach, where the contact
with the heat bath is simulated by the Glauber stochastic dynamics. The phase diagram of the model is constructed from the
stationary values of the magnetization as a function of temperature and field amplitude. The continuous phase transitions
coincide with the equilibrium ones, while the first-order transitions occur at fields larger than the corresponding values
at equilibrium. The difference between the fields at the limit of stability of the ordered phase and that of the equilibrium
is maximum at zero temperature and vanishes at the tricritical point. We also find the mean field time auto-correlation function
at the stationary states of the model.
Received: 4 June 1997 / Revised: 5 August 1997 / Accepted: 10 November 1997 相似文献
7.
R. Paul M. Alava H. Rieger 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,30(3):357-367
The random field q-states Potts model is investigated using exact groundstates and finite-temperature transfer matrix calculations. It is found
that the domain structure and the Zeeman energy of the domains resembles for general q the random field Ising case (q = 2). This is also the expected outcome based on a random-walk picture of the groundstate. The domain size distribution is
exponential, and the scaling of the average domain size with the disorder strength is similar for q arbitrary. The zero-temperature properties are compared to the equilibrium spin states at small temperatures, to investigate
the effect of local random field fluctuations that imply locally degenerate regions. The response to field perturbations (`chaos')
and the susceptibility are investigated. In particular for the chaos exponent it is found to be 1 for q = 2,..., 5. Finally for q = 2 (Ising case) the domain length distribution is studied for correlated random fields.
Received 27 August 2002 Published online 19 December 2002
RID="a"
ID="a"e-mail: rieger@lusi-sb.de 相似文献
8.
The singularity of the specific heat is studied for the dilution (J>J'>0) type and Gaussian type random Ising models using the Pfaffian method numerically. The type of singularity at the paramagnetic-ferromagnetic
phase boundary is studied using the standard regression method using data up to system size. It is shown that the logarithmic type singularity is more reliable than the double-logarithmic type and cusp
type singularities. The critical temperatures are estimated accurately for both the dilution type and Gaussian type random
Ising models. A phase diagram relating strength of the randomness and temperature is also presented.
Received: 26 February 1998 / Revised: 15 May 1998 / Accepted: 25 June 1998 相似文献
9.
N. G. Fytas A. Malakis 《The European Physical Journal B - Condensed Matter and Complex Systems》2011,79(1):13-20
We investigate, by means of extensive Monte Carlo
simulations, the magnetic critical behavior of the
three-dimensional bimodal random-field Ising model at the strong
disorder regime. We present results in favor of the two-exponent
scaling scenario, [`(h)]\bar{\eta} = 2η, where η and
[`(h)]\bar{\eta} are the critical exponents describing the power-law
decay of the connected and disconnected correlation functions and
we illustrate, using various finite-size measures and properly
defined noise to signal ratios, the strong violation of
self-averaging of the model in the ordered phase. 相似文献
10.
On the properties of small-world network models 总被引:7,自引:0,他引:7
A. Barrat M. Weigt 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,13(3):547-560
We study the small-world networks recently introduced by Watts and Strogatz [Nature 393, 440 (1998)], using analytical as well as numerical tools. We characterize the geometrical properties resulting from the
coexistence of a local structure and random long-range connections, and we examine their evolution with size and disorder
strength. We show that any finite value of the disorder is able to trigger a “small-world” behaviour as soon as the initial
lattice is big enough, and study the crossover between a regular lattice and a “small-world” one. These results are corroborated
by the investigation of an Ising model defined on the network, showing for every finite disorder fraction a crossover from
a high-temperature region dominated by the underlying one-dimensional structure to a mean-field like low-temperature region.
In particular there exists a finite-temperature ferromagnetic phase transition as soon as the disorder strength is finite.
[0.5cm]
Received 29 March 1999 and Received in final form 21 May 1999 相似文献
11.
Nikolaos G. Fytas Víctor Martín-Mayor Marco Picco Nicolas Sourlas 《Journal of statistical physics》2018,172(2):665-672
A lot of progress has been made recently in our understanding of the random-field Ising model thanks to large-scale numerical simulations. In particular, it has been shown that, contrary to previous statements: the critical exponents for different probability distributions of the random fields and for diluted antiferromagnets in a field are the same. Therefore, critical universality, which is a perturbative renormalization-group prediction, holds beyond the validity regime of perturbation theory. Most notably, dimensional reduction is restored at five dimensions, i.e., the exponents of the random-field Ising model at five dimensions and those of the pure Ising ferromagnet at three dimensions are the same. 相似文献
12.
V. Janiš 《Journal of statistical physics》1987,47(5-6):931-938
Within the perturbation diagrammatic expansion we discuss the origin of differences in determinations of the lower critical dimension of the random-field Ising model and show that below four dimensions metastability and hysteresis occur. We also explain the occurrence of a quasicritical d=2 behavior at weak random fields, which is responsible for local stability of the ordered state above two dimensions. 相似文献
13.
We study the effect of quantum fluctuations in an Ising
spin system on a scale-free network of
degree exponent γ>5 using
a quantum Monte Carlo simulation technique. In our model,
one can adjust the magnitude of the magnetic field perpendicular
to the Ising spin direction and can therefore control the
strength of quantum fluctuations for
each spin. Our numerical analysis
shows that quantum fluctuations reduce the transition
temperature Tc of the ferromagnetic-paramagnetic phase
transition. However, the phase transition belongs to
the same mean-field type universality class both with
and without the quantum fluctuations.
We also study the role of hubs by turning on the
quantum fluctuations exclusively
at the nodes with the most links. When only a small number of hub
spins fluctuate quantum mechanically, Tc
decreases with increasing magnetic field
until it saturates at high fields. This effect
becomes stronger as the number of hub spins increases.
In contrast, quantum fluctuations at the same number of
“non-hub” spins do not affect Tc. This implies
that the hubs play an important role in
maintaining order in the whole network. 相似文献
14.
B. Drossel K. Dahmen 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,3(4):485-496
We report studies of the behaviour of a single driven domain wall in the 2-dimensional non-equilibrium zero temperature random-field
Ising model, closely above the depinning threshold. It is found that even for very weak disorder, the domain wall moves through
the system in percolative fashion. At depinning, the fraction of spins that are flipped by the proceeding avalanche vanishes
with the same exponent as the infinite percolation cluster in percolation theory. With decreasing disorder strength, however, the size of the critical
region decreases. Our numerical simulation data appear to reflect a crossover behaviour to an exponent at zero disorder strength. The conclusions of this paper strongly rely on analytical arguments. A scaling theory in terms
of the disorder strength and the magnetic field is presented that gives the values of all critical exponent except for one,
the value of which is estimated from scaling arguments.
Received: 13 February 1998 / Accepted: 30 March 1998 相似文献
15.
We show that the critical behavior of a colloid-polymer mixture inside a random porous matrix of quenched hard spheres belongs to the universality class of the random-field Ising model. We also demonstrate that random-field effects in colloid-polymer mixtures are surprisingly strong. This makes these systems attractive candidates to study random-field behavior experimentally. 相似文献
16.
Some results on NMR and relaxation studies of the Van Vleck paramagnet TmES (thulium ethylsulphate) and the Ising ferromagnet
DyES are summarized. Complicated but regular quasistatic internal magnetic fields are created by Tm and Dy ions in these compounds.
These fields fluctuate due to the thermal excitation of tne ions and the energy transfer from one ion to another. Fluctuations
give rise to NMR line shifts, broadening of the lines and spin-lattice relaxation, the shifts, linewidth and spin-lattice
relaxation rate being proportional to exp(−Δ/kT) at low temperatures (kT≪Δ, Δ is an excitation energy). Pre-exponential factors
depend on fluctuating fields in a definite but complicated manner, so estimates of the correlation time (electron spin-spin
relaxation time) can be obtained from measurements of nuclear relaxation rates. 相似文献
17.
The transverse random-field Ising model with a trimodal distribution is studied within mean-field and mean-field renormalization-group approaches. The phase diagram is obtained and all the transition lines are second order. An ordered phase persists for large random fields provided that the probability of the zero transverse field is greater than the site-percolation threshold. 相似文献
18.
We investigate the low-temperature critical behavior of the three-dimensional random-field Ising ferromagnet. By a scaling analysis we find that in the limit of temperature T → 0 the usual scaling relations have to be modified as far as the exponent α of the specific heat is concerned. At zero temperature, the Rushbrooke equation is modified to α + 2β + γ = 1, an equation which we expect to be valid also for other systems with similar critical behavior. We test the scaling theory numerically for the three-dimensional random-field Ising system with Gaussian probability distribution of the random fields by a combination of calculations of exact ground states with an integer optimization algorithm and Monte Carlo methods. By a finite-size scaling analysis we calculate the critical exponents ν ≈ 1.0, β ≈ 0.05,
≈ 2.9, γ ≈ 1.5 and α ≈ −0.55. 相似文献
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19.
C. Monthus T. Garel 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,53(1):39-45
The directed polymer in a 1+3 dimensional
random medium is known to present a disorder-induced phase
transition. For a polymer of length L, the high temperature
phase is characterized by a diffusive behavior for the end-point
displacement R2 ∼L and by free-energy fluctuations of order
ΔF(L) ∼O(1). The low-temperature phase is characterized by
an anomalous wandering exponent R2/L ∼Lω and
by free-energy fluctuations of order ΔF(L) ∼Lω
where ω∼0.18. In this paper, we first study the scaling
behavior of various properties to localize the critical temperature
Tc. Our results concerning R2/L and ΔF(L) point towards
0.76 < Tc ≤T2=0.79, so our conclusion is that Tc is equal
or very close to the upper bound T2 derived by Derrida and
coworkers (T2 corresponds to the temperature above which the ratio
remains finite as L ↦
∞). We then present histograms for the free-energy, energy and
entropy over disorder samples. For T ≫Tc, the free-energy
distribution is found to be Gaussian. For T ≪Tc, the free-energy
distribution coincides with the ground state energy distribution, in
agreement with the zero-temperature fixed point picture. Moreover the
entropy fluctuations are of order ΔS ∼L1/2 and follow a
Gaussian distribution, in agreement with the droplet predictions,
where the free-energy term ΔF ∼Lω is a near
cancellation of energy and entropy contributions of order L1/2. 相似文献