232,209 research outputs found
The many-body localization phase transition
We use exact diagonalization to explore the many-body localization transition
in a random-field spin-1/2 chain. We examine the correlations within each
many-body eigenstate, looking at all high-energy states and thus effectively
working at infinite temperature. For weak random field the eigenstates are
thermal, as expected in this nonlocalized, "ergodic" phase. For strong random
field the eigenstates are localized, with only short-range entanglement. We
roughly locate the localization transition and examine some of its finite-size
scaling, finding that this quantum phase transition at nonzero temperature
might be showing infinite-randomness scaling with a dynamic critical exponent
.Comment: 7 pages, 8 figures. Extended version of arXiv:1003.2613v
Phase diagram of a random-anisotropy mixed-spin Ising model
We investigate the phase diagram of a mixed spin-1/2--spin-1 Ising system in
the presence of quenched disordered anisotropy. We carry out a mean-field and a
standard self-consistent Bethe--Peierls calculation. Depending on the amount of
disorder, there appear novel transition lines and multicritical points. Also,
we report some connections with a percolation problem and an exact result in
one dimension.Comment: 8 pages, 4 figures, accepted for publication in Physical Review
Universality in Random Walk Models with Birth and Death
Models of random walks are considered in which walkers are born at one
location and die at all other locations with uniform death rate. Steady-state
distributions of random walkers exhibit dimensionally dependent critical
behavior as a function of the birth rate. Exact analytical results for a
hyperspherical lattice yield a second-order phase transition with a nontrivial
critical exponent for all positive dimensions . Numerical studies
of hypercubic and fractal lattices indicate that these exact results are
universal. Implications for the adsorption transition of polymers at curved
interfaces are discussed.Comment: 11 pages, revtex, 2 postscript figure
Conjectured Exact Percolation Thresholds of the Fortuin-Kasteleyn Cluster for the +-J Ising Spin Glass Model
The conjectured exact percolation thresholds of the Fortuin-Kasteleyn cluster
for the +-J Ising spin glass model are theoretically shown based on a
conjecture. It is pointed out that the percolation transition of the
Fortuin-Kasteleyn cluster for the spin glass model is related to a dynamical
transition for the freezing of spins. The present results are obtained as
locations of points on the so-called Nishimori line, which is a special line in
the phase diagram. We obtain TFK = 2 / ln [z / (z - 2)] and pFK = z / [2 (z -
1)] for the Bethe lattice, TFK -> infinity and pFK -> 1 / 2 for the
infinite-range model, TFK = 2 / ln 3 and pFK = 3 / 4 for the square lattice,
TFK ~ 3.9347 and pFK ~ 0.62441 for the simple cubic lattice, TFK ~ 6.191 and
pFK ~ 0.5801 for the 4-dimensional hypercubic lattice, and TFK = 2 / ln {[1 + 2
sin (pi / 18)] / [1 - 2 sin (pi / 18) ]} and pFK = [1 + 2 sin (pi / 18) ] / 2
for the triangular lattice, when J / kB = 1, where z is the coordination
number, J is the strength of the exchange interaction between spins, kB is the
Boltzmann constant, TFK is the temperature at the percolation transition point,
and pFK is the probability, that the interaction is ferromagnetic, at the
percolation transition point.Comment: 10 pages, 1 figure. v8: this is the final versio
Analytical evidence for the absence of spin glass transition on self-dual lattices
We show strong evidence for the absence of a finite-temperature spin glass
transition for the random-bond Ising model on self-dual lattices. The analysis
is performed by an application of duality relations, which enables us to derive
a precise but approximate location of the multicritical point on the Nishimori
line. This method can be systematically improved to presumably give the exact
result asymptotically. The duality analysis, in conjunction with the
relationship between the multicritical point and the spin glass transition
point for the symmetric distribution function of randomness, leads to the
conclusion of the absence of a finite-temperature spin glass transition for the
case of symmetric distribution. The result is applicable to the random bond
Ising model with or Gaussian distribution and the Potts gauge glass on
the square, triangular and hexagonal lattices as well as the random three-body
Ising model on the triangular and the Union-Jack lattices and the four
dimensional random plaquette gauge model. This conclusion is exact provided
that the replica method is valid and the asymptotic limit of the duality
analysis yields the exact location of the multicritical pointComment: 11 Pages, 4 figures, 1 table. submitted to J. Phys. A Math. Theo
Many-body localization phase transition
We use exact diagonalization to explore the many-body localization transition in a random-field spin-1/2
chain. We examine the correlations within each many-body eigenstate, looking at all high-energy states and
thus effectively working at infinite temperature. For weak random field the eigenstates are thermal, as expected
in this nonlocalized, âergodicâ phase. For strong random field the eigenstates are localized with only shortrange entanglement. We roughly locate the localization transition and examine some of its finite-size scaling,
finding that this quantum phase transition at nonzero temperature might be showing infinite-randomness scaling with a dynamic critical exponent zâïżœ
From Disordered Crystal to Glass: Exact Theory
We calculate thermodynamic properties of a disordered model insulator,
starting from the ideal simple-cubic lattice () and increasing the
disorder parameter to . As in earlier Einstein- and Debye-
approximations, there is a phase transition at . For the
low-T heat-capacity whereas for , . The van
Hove singularities disappear at {\em any finite }. For we discover
novel {\em fixed points} in the self-energy and spectral density of this model
glass.Comment: Submitted to Phys. Rev. Lett., 8 pages, 4 figure
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