443 research outputs found
Field-Driven Hysteresis of the d=3 Ising Spin Glass: Hard-Spin Mean-Field Theory
Hysteresis loops are obtained in the Ising spin-glass phase in d=3, using
frustration-conserving hard-spin mean-field theory. The system is driven by a
time-dependent random magnetic field H_Q that is conjugate to the spin-glass
order Q, yielding a field-driven first-order phase transition through the
spin-glass phase. The hysteresis loop area A of the Q-H_Q curve scales with
respect to the sweep rate h of magnetic field as A-A_0 = h^b. In the spin-glass
and random-bond ferromagnetic phases, the sweep-rate scaling exponent b changes
with temperature T, but appears not to change with antiferromagnetic bond
concentration p. By contrast, in the pure ferromagnetic phase, b does not
depend on T and has a sharply different value than in the two other phases.Comment: 5 pages, 8 figures, 1 table. Replaced with published versio
Strongly Asymmetric Tricriticality of Quenched Random-Field Systems
In view of the recently seen dramatic effect of quenched random bonds on
tricritical systems, we have conducted a renormalization-group study on the
effect of quenched random fields on the tricritical phase diagram of the spin-1
Ising model in . We find that random fields convert first-order phase
transitions into second-order, in fact more effectively than random bonds. The
coexistence region is extremely flat, attesting to an unusually small
tricritical exponent ; moreover, an extreme asymmetry of the phase
diagram is very striking. To accomodate this asymmetry, the second-order
boundary exhibits reentrance.Comment: revtex, 4 pages, 2 figs, submitted to PR
Universality aspects of the d=3 random-bond Blume-Capel model
The effects of bond randomness on the universality aspects of the simple
cubic lattice ferromagnetic Blume-Capel model are discussed. The system is
studied numerically in both its first- and second-order phase transition
regimes by a comprehensive finite-size scaling analysis. We find that our data
for the second-order phase transition, emerging under random bonds from the
second-order regime of the pure model, are compatible with the universality
class of the 3d random Ising model. Furthermore, we find evidence that, the
second-order transition emerging under bond randomness from the first-order
regime of the pure model, belongs to a new and distinctive universality class.
The first finding reinforces the scenario of a single universality class for
the 3d Ising model with the three well-known types of quenched uncorrelated
disorder (bond randomness, site- and bond-dilution). The second, amounts to a
strong violation of universality principle of critical phenomena. For this case
of the ex-first-order 3d Blume-Capel model, we find sharp differences from the
critical behaviors, emerging under randomness, in the cases of the
ex-first-order transitions of the corresponding weak and strong first-order
transitions in the 3d three-state and four-state Potts models.Comment: 12 pages, 12 figure
Deep Spin-Glass Hysteresis Area Collapse and Scaling in the Ising Model
We investigate the dissipative loss in the Ising spin glass in three
dimensions through the scaling of the hysteresis area, for a maximum magnetic
field that is equal to the saturation field. We perform a systematic analysis
for the whole range of the bond randomness as a function of the sweep rate, by
means of frustration-preserving hard-spin mean field theory. Data collapse
within the entirety of the spin-glass phase driven adiabatically (i.e.,
infinitely-slow field variation) is found, revealing a power-law scaling of the
hysteresis area as a function of the antiferromagnetic bond fraction and the
temperature. Two dynamic regimes separated by a threshold frequency
characterize the dependence on the sweep rate of the oscillating field. For
, the hysteresis area is equal to its value in the adiabatic
limit , while for it increases with the
frequency through another randomness-dependent power law.Comment: 6 pages, 6 figure
Uncovering the secrets of the 2d random-bond Blume-Capel model
The effects of bond randomness on the ground-state structure, phase diagram
and critical behavior of the square lattice ferromagnetic Blume-Capel (BC)
model are discussed. The calculation of ground states at strong disorder and
large values of the crystal field is carried out by mapping the system onto a
network and we search for a minimum cut by a maximum flow method. In finite
temperatures the system is studied by an efficient two-stage Wang-Landau (WL)
method for several values of the crystal field, including both the first- and
second-order phase transition regimes of the pure model. We attempt to explain
the enhancement of ferromagnetic order and we discuss the critical behavior of
the random-bond model. Our results provide evidence for a strong violation of
universality along the second-order phase transition line of the random-bond
version.Comment: 6 LATEX pages, 3 EPS figures, Presented by AM at the symposium
"Trajectories and Friends" in honor of Nihat Berker, MIT, October 200
d=3 Anisotropic and d=2 tJ Models: Phase Diagrams, Thermodynamic Properties, and Chemical Potential Shift
The anisotropic d=3 tJ model is studied by renormalization-group theory,
yielding the evolution of the system as interplane coupling is varied from the
isotropic three-dimensional to quasi-two-dimensional regimes.
Finite-temperature phase diagrams, chemical potential shifts, and in-plane and
interplane kinetic energies and antiferromagnetic correlations are calculated
for the entire range of electron densities. We find that the novel tau phase,
seen in earlier studies of the isotropic d=3 tJ model, and potentially
corresponding to the superconducting phase in high-T_c materials, persists even
for strong anisotropy. While the tau phase appears at low temperatures at
30-35% hole doping away from =1, at smaller hole dopings we see a complex
lamellar structure of antiferromagnetic and disordered regions, with a
suppressed chemical potential shift, a possible marker of incommensurate
ordering in the form of microscopic stripes. An investigation of the
renormalization-group flows for the isotropic two-dimensional tJ model also
shows a pre-signature of the tau phase, which appears with finite transition
temperatures upon addition of the smallest interplane coupling.Comment: 13 pages, 7 figures; replaced with published versio
Fractal Measures of Sea, Lake, Strait, and Dam-Reserve Shores: Calculation, Differentiation, and Interpretation
The fractal dimensions d_f of the shore lines of the Mediterranean, the
Aegean, the Black Sea, the Bosphorus Straits (on both the Asian and European
sides), the Van Lake, and the lake formed by the Ataturk Dam have been
calculated. Important distinctions have been found and explained.Comment: 3 pages, 2 figures, 1 tabl
An Analytic Equation of State for Ising-like Models
Using an Environmentally Friendly Renormalization we derive, from an
underlying field theory representation, a formal expression for the equation of
state, , that exhibits all desired asymptotic and analyticity
properties in the three limits , and . The only
necessary inputs are the Wilson functions , and
, associated with a renormalization of the transverse vertex
functions. These Wilson functions exhibit a crossover between the Wilson-Fisher
fixed point and the fixed point that controls the coexistence curve.
Restricting to the case N=1, we derive a one-loop equation of state for naturally parameterized by a ratio of non-linear scaling fields. For
we show that a non-parameterized analytic form can be deduced. Various
asymptotic amplitudes are calculated directly from the equation of state in all
three asymptotic limits of interest and comparison made with known results. By
positing a scaling form for the equation of state inspired by the one-loop
result, but adjusted to fit the known values of the critical exponents, we
obtain better agreement with known asymptotic amplitudes.Comment: 10 pages, 2 figure
Two Superconducting Phases in the d=3 Hubbard Model: Phase Diagram and Specific Heat from Renormalization-Group Calculations
The phase diagram of the d=3 Hubbard model is calculated as a function of
temperature and electron density n_i, in the full range of densities between 0
and 2 electrons per site, using renormalization-group theory. An
antiferromagnetic phase occurs at lower temperatures, at and near the
half-filling density of = 1. The antiferromagnetic phase is unstable to
hole or electron doping of at most 15%, yielding to two distinct "tau" phases:
for large coupling U/t, one such phase occurs between 30-35% hole or electron
doping, and for small to intermediate coupling U/t another such phase occurs
between 10-18% doping. Both tau phases are distinguished by non-zero hole or
electron hopping expectation values at all length scales. Under further doping,
the tau phases yield to hole- or electron-rich disordered phases. We have
calculated the specific heat over the entire phase diagram. The low-temperature
specific heat of the weak-coupling tau phase shows a BCS-type exponential
decay, indicating a gap in the excitation spectrum, and a cusp singularity at
the phase boundary. The strong-coupling tau phase, on the other hand, has
characteristics of BEC-type superconductivity, including a critical exponent
alpha approximately equal to -1, and an additional peak in the specific heat
above the transition temperature indicating pair formation. In the limit of
large Coulomb repulsion, the phase diagram of the tJ model is recovered.Comment: 16 pages, 10 figures; typos in Fig. 2 correcte
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