248 research outputs found
The random-field specific heat critical behavior at high magnetic concentration: Fe(0.93)Zn(0.07)F2
The specific heat critical behavior is measured and analyzed for a single
crystal of the random-field Ising system Fe(0.93)Zn(0.07)F2 using pulsed heat
and optical birefringence techniques. This high magnetic concentration sample
does not exhibit the severe scattering hysteresis at low temperature seen in
lower concentration samples and its behavior is therefore that of an
equilibrium random-field Ising model system. The equivalence of the behavior
observed with pulsed heat techniques and optical birefringence is established.
The critical peak appears to be a symmetric, logarithmic divergence, in
disagreement with random-field model computer simulations. The random-field
specific heat scaling function is determined.Comment: 9 pages, 4 figures, RevTeX, minor revision
Ordering in the dilute weakly-anisotropic antiferromagnet Mn(0.35)Zn(0.65)F2
The highly diluted antiferromagnet Mn(0.35)Zn(0.65)F2 has been investigated
by neutron scattering in zero field. The Bragg peaks observed below the Neel
temperature TN (approximately 10.9 K) indicate stable antiferromagnetic
long-range ordering at low temperature. The critical behavior is governed by
random-exchange Ising model critical exponents (nu approximately 0.69 and gamma
approximately 1.31), as reported for Mn(x)Zn(1-x)F2 with higher x and for the
isostructural compound Fe(x)Zn(1-x)F2. However, in addition to the Bragg peaks,
unusual scattering behavior appears for |q|>0 below a glassy temperature Tg
approximately 7.0 K. The glassy region T<Tg corresponds to that of noticeable
frequency dependence in earlier zero-field ac susceptibility measurements on
this sample. These results indicate that long-range order coexists with
short-range nonequilibrium clusters in this highly diluted magnet.Comment: 7 pages, 5 figure
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
Ground state non-universality in the random field Ising model
Two attractive and often used ideas, namely universality and the concept of a
zero temperature fixed point, are violated in the infinite-range random-field
Ising model. In the ground state we show that the exponents can depend
continuously on the disorder and so are non-universal. However, we also show
that at finite temperature the thermal order parameter exponent one half is
restored so that temperature is a relevant variable. The broader implications
of these results are discussed.Comment: 4 pages 2 figures, corrected prefactors caused by a missing factor of
two in Eq. 2., added a paragraph in conclusions for clarit
Effects of Pore Walls and Randomness on Phase Transitions in Porous Media
We study spin models within the mean field approximation to elucidate the
topology of the phase diagrams of systems modeling the liquid-vapor transition
and the separation of He--He mixtures in periodic porous media. These
topologies are found to be identical to those of the corresponding random field
and random anisotropy spin systems with a bimodal distribution of the
randomness. Our results suggest that the presence of walls (periodic or
otherwise) are a key factor determining the nature of the phase diagram in
porous media.Comment: REVTeX, 11 eps figures, to appear in Phys. Rev.
Properties of the random field Ising model in a transverse magnetic field
We consider the effect of a random longitudinal field on the Ising model in a
transverse magnetic field. For spatial dimension , there is at low
strength of randomness and transverse field, a phase with true long range order
which is destroyed at higher values of the randomness or transverse field. The
properties of the quantum phase transition at zero temperature are controlled
by a fixed point with no quantum fluctuations. This fixed point also controls
the classical finite temperature phase transition in this model. Many critical
properties of the quantum transition are therefore identical to those of the
classical transition. In particular, we argue that the dynamical scaling is
activated, i.e, the logarithm of the diverging time scale rises as a power of
the diverging length scale
Percolation on two- and three-dimensional lattices
In this work we apply a highly efficient Monte Carlo algorithm recently
proposed by Newman and Ziff to treat percolation problems. The site and bond
percolation are studied on a number of lattices in two and three dimensions.
Quite good results for the wrapping probabilities, correlation length critical
exponent and critical concentration are obtained for the square, simple cubic,
HCP and hexagonal lattices by using relatively small systems. We also confirm
the universal aspect of the wrapping probabilities regarding site and bond
dilution.Comment: 15 pages, 6 figures, 3 table
Dynamic structure factor of the Ising model with purely relaxational dynamics
We compute the dynamic structure factor for the Ising model with a purely
relaxational dynamics (model A). We perform a perturbative calculation in the
expansion, at two loops in the high-temperature phase and at one
loop in the temperature magnetic-field plane, and a Monte Carlo simulation in
the high-temperature phase. We find that the dynamic structure factor is very
well approximated by its mean-field Gaussian form up to moderately large values
of the frequency and momentum . In the region we can investigate,
, , where is the correlation
length and the zero-momentum autocorrelation time, deviations are at
most of a few percent.Comment: 21 pages, 3 figure
Revisiting the scaling of the specific heat of the three-dimensional random-field Ising model
We revisit the scaling behavior of the specific heat of the three-dimensional
random-field Ising model with a Gaussian distribution of the disorder. Exact ground states
of the model are obtained using graph-theoretical algorithms for different strengths
= 268 3Â spins. By numerically differentiating the bond energy
with respect to h, a specific-heat-like quantity is obtained whose
maximum is found to converge to a constant in the thermodynamic limit. Compared to a
previous study following the same approach, we have studied here much larger system sizes
with an increased statistical accuracy. We discuss the relevance of our results under the
prism of a modified Rushbrooke inequality for the case of a saturating specific heat.
Finally, as a byproduct of our analysis, we provide high-accuracy estimates of the
critical field hc =
2.279(7) and the critical exponent of the correlation exponent
Μ =
1.37(1), in excellent agreement to the most recent computations in the
literature
The three-dimensional randomly dilute Ising model: Monte Carlo results
We perform a high-statistics simulation of the three-dimensional randomly
dilute Ising model on cubic lattices with . We choose a
particular value of the density, x=0.8, for which the leading scaling
corrections are suppressed. We determine the critical exponents, obtaining , , , and ,
in agreement with previous numerical simulations. We also estimate numerically
the fixed-point values of the four-point zero-momentum couplings that are used
in field-theoretical fixed-dimension studies. Although these results somewhat
differ from those obtained using perturbative field theory, the
field-theoretical estimates of the critical exponents do not change
significantly if the Monte Carlo result for the fixed point is used. Finally,
we determine the six-point zero-momentum couplings, relevant for the
small-magnetization expansion of the equation of state, and the invariant
amplitude ratio that expresses the universality of the free-energy
density per correlation volume. We find .Comment: 34 pages, 7 figs, few correction
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