873 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
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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
Maximally Random Discrete-Spin Systems with Symmetric and Asymmetric Interactions and Maximally Degenerate Ordering
Discrete-spin systems with maximally random nearest-neighbor interactions
that can be symmetric or asymmetric, ferromagnetic or antiferromagnetic,
including off-diagonal disorder, are studied, for the number of states
in dimensions. We use renormalization-group theory that is exact for
hierarchical lattices and approximate (Migdal-Kadanoff) for hypercubic
lattices. For all d>1 and all non-infinite temperatures, the system eventually
renormalizes to a random single state, thus signaling qxq degenerate ordering.
Note that this is the maximally degenerate ordering. For high-temperature
initial conditions, the system crosses over to this highly degenerate ordering
only after spending many renormalization-group iterations near the disordered
(infinite-temperature) fixed point. Thus, a temperature range of short-range
disorder in the presence of long-range order is identified, as previously seen
in underfrustrated Ising spin-glass systems. The entropy is calculated for all
temperatures, behaves similarly for ferromagnetic and antiferromagnetic
interactions, and shows a derivative maximum at the short-range disordering
temperature. With a sharp immediate contrast of infinitesimally higher
dimension 1+\epsilon, the system is as expected disordered at all temperatures
for d=1.Comment: Final published version, 4 pages, 5 figure
The Chiral Potts Spin Glass in d=2 and 3 Dimensions
The chiral spin-glass Potts system with q=3 states is studied in d=2 and 3
spatial dimensions by renormalization-group theory and the global phase
diagrams are calculated in temperature, chirality concentration p, and
chirality-breaking concentration c, with determination of phase chaos and
phase-boundary chaos. In d=3, the system has ferromagnetic, left-chiral,
right-chiral, chiral spin-glass, and disordered phases. The phase boundaries to
the ferromagnetic, left- and right-chiral phases show, differently, an unusual,
fibrous patchwork (microreentrances) of all four (ferromagnetic, left-chiral,
right-chiral, chiral spin-glass) ordered ordered phases, especially in the
multicritical region. The chaotic behavior of the interactions, under scale
change, are determined in the chiral spin-glass phase and on the boundary
between the chiral spin-glass and disordered phases, showing Lyapunov exponents
in magnitudes reversed from the usual ferromagnetic-antiferromagnetic
spin-glass systems. At low temperatures, the boundaries of the left- and
right-chiral phases become thresholded in p and c. In the d=2, the chiral
spin-glass system does not have a spin-glass phase, consistently with the
lower-critical dimension of ferromagnetic-antiferromagnetic spin glasses. The
left- and right-chirally ordered phases show reentrance in chirality
concentration p.Comment: 9 pages, 7 figures, 19 phase diagrams. Final published versio
Inverted Berezinskii-Kosterlitz-Thouless Singularity and High-Temperature Algebraic Order in an Ising Model on a Scale-Free Hierarchical-Lattice Small-World Network
We have obtained exact results for the Ising model on a hierarchical lattice
with a scale-free degree distribution, high clustering coefficient, and
small-world behavior. By varying the probability p of long-range bonds, the
entire spectrum from an unclustered, non-small-world network to a
highly-clustered, small-world system is studied. We obtain analytical
expressions for the degree distribution P(k) and clustering coefficient C for
all p, as well as the average path length l for p=0 and 1. The Ising model on
this network is studied through an exact renormalization-group transformation
of the quenched bond probability distribution, using up to 562,500 probability
bins to represent the distribution. For p < 0.494, we find power-law critical
behavior of the magnetization and susceptibility, with critical exponents
continuously varying with p, and exponential decay of correlations away from
T_c. For p >= 0.494, where the network exhibits small-world character, the
critical behavior radically changes: We find a highly unusual phase transition,
namely an inverted Berezinskii-Kosterlitz-Thouless singularity, between a
low-temperature phase with non-zero magnetization and finite correlation length
and a high-temperature phase with zero magnetization and infinite correlation
length. Approaching T_c from below, the magnetization and the susceptibility
respectively exhibit the singularities of exp(-C/sqrt(T_c-T)) and
exp(D/sqrt(T_c-T)), with C and D positive constants. With long-range bond
strengths decaying with distance, we see a phase transition with power-law
critical singularities for all p, an unusually narrow critical region and
important corrections to power-law behavior that depend on the exponent
characterizing the decay of long-range interactions.Comment: 22 pages, 19 figures; replaced with published versio
Successively Thresholded Domain Boundary Roughening Driven by Pinning Centers and Missing Bonds: Hard-Spin Mean-Field Theory Applied to d=3 Ising Magnets
Hard-spin mean-field theory has recently been applied to Ising magnets,
correctly yielding the absence and presence of an interface roughening
transition respectively in and dimensions and producing the
ordering-roughening phase diagram for isotropic and anisotropic systems. The
approach has now been extended to the effects of quenched random pinning
centers and missing bonds on the interface of isotropic and anisotropic Ising
models in . We find that these frozen impurities cause domain boundary
roughening that exhibits consecutive thresholding transitions as a function
interaction of anisotropy. For both missing-bond and pinning-center impurities,
for moderately large values the anisotropy, the systems saturate to the
"solid-on-solid" limit, exhibiting a single universal curve for the domain
boundary width as a function of impurity concentration.Comment: Published version, 4 pages, 5 figure
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