21,753 research outputs found
On the Incommensurate Phase in Modulated Heisenberg Chains
Using the density matrix renormalization group method (DMRG) we calculate the
magnetization of frustrated S=1/2 Heisenberg chains for various modulation
patterns of the nearest neighbour coupling: commensurate, incommensurate with
sinusoidal modulation and incommensurate with solitonic modulation. We focus on
the order of the phase transition from the commensurate dimerized phase (D) to
the incommensurate phase (I). It is shown that the order of the phase
transition depends sensitively on the model. For the solitonic model in
particular, a -dependent elastic energy modifies the order of the
transition. Furthermore, we calculate gaps in the incommensurate phase in
adiabatic approximation.Comment: 8 pages, 9 figure
Ground-state clusters of two-, three- and four-dimensional +-J Ising spin glasses
A huge number of independent true ground-state configurations is calculated
for two-, three- and four-dimensional +- J spin-glass models. Using the genetic
cluster-exact approximation method, system sizes up to N=20^2,8^3,6^4 spins are
treated. A ``ballistic-search'' algorithm is applied which allows even for
large system sizes to identify clusters of ground states which are connected by
chains of zero-energy flips of spins. The number of clusters n_C diverges with
N going to infinity. For all dimensions considered here, an exponential
increase of n_C appears to be more likely than a growth with a power of N. The
number of different ground states is found to grow clearly exponentially with
N. A zero-temperature entropy per spin of s_0=0.078(5)k_B (2d), s_0=0.051(3)k_B
(3d) respectively s_0=0.027(5)k_B (4d) is obtained.Comment: large extensions, now 12 pages, 9 figures, 27 reference
Direct sampling of complex landscapes at low temperatures: the three-dimensional +/-J Ising spin glass
A method is presented, which allows to sample directly low-temperature
configurations of glassy systems, like spin glasses. The basic idea is to
generate ground states and low lying excited configurations using a heuristic
algorithm. Then, with the help of microcanonical Monte Carlo simulations, more
configurations are found, clusters of configurations are determined and
entropies evaluated. Finally equilibrium configuration are randomly sampled
with proper Gibbs-Boltzmann weights.
The method is applied to three-dimensional Ising spin glasses with +- J
interactions and temperatures T<=0.5. The low-temperature behavior of this
model is characterized by evaluating different overlap quantities, exhibiting a
complex low-energy landscape for T>0, while the T=0 behavior appears to be less
complex.Comment: 9 pages, 7 figures, revtex (one sentence changed compared to v2
Reply to the Comment on `Glassy Transition in a Disordered Model for the RNA Secondary Structure'
We reply to the Comment by Hartmann (cond-mat/9908132) on our paper Phys.
Rev. Lett. 84 (2000) 2026 (also cond-mat/9907125).Comment: 1 page, no figures. Accepted for publication in Phys. Rev. Let
Cerenkov-electrooptic shutter--a subnanosecond intense, relativistic electron beam diagnostic
No spin-glass transition in the "mobile-bond" model
The recently introduced ``mobile-bond'' model for two-dimensional spin
glasses is studied. The model is characterized by an annealing temperature T_q.
On the basis of Monte Carlo simulations of small systems it has been claimed
that this model exhibits a non-trivial spin-glass transition at finite
temperature for small values of T_q.
Here the model is studied by means of exact ground-state calculations of
large systems up to N=256^2. The scaling of domain-wall energies is
investigated as a function of the system size. For small values T_q<0.95 the
system behaves like a (gauge-transformed) ferromagnet having a small fraction
of frustrated plaquettes. For T_q>=0.95 the system behaves like the standard
two-dimensional +-J spin-glass, i.e. it does NOT exhibit a phase transition at
T>0.Comment: 4 pages, 5 figures, RevTe
Systematic Mapping of the Hubbard Model to the Generalized t-J Model
The generalized t-J model conserving the number of double occupancies is
constructed from the Hubbard model at and in the vicinity of half-filling at
strong coupling. The construction is realized by a self-similar continuous
unitary transformation. The flow equation is closed by a truncation scheme
based on the spatial range of processes. We analyze the conditions under which
the t-J model can be set up and we find that it can only be defined for
sufficiently large interaction. There, the parameters of the effective model
are determined.Comment: 16 pages, 13 figures included. v2: Order of sections changed.
Calculation and discussion of apparent gap in Section IV.A correcte
Correct extrapolation of overlap distribution in spin glasses
We study in d=3 dimensions the short range Ising spin glass with Jij=+/-1
couplings at T=0. We show that the overlap distribution is non-trivial in the
limit of large system size.Comment: 6 pages, 3 figure
A new method for analyzing ground-state landscapes: ballistic search
A ``ballistic-search'' algorithm is presented which allows the identification
of clusters (or funnels) of ground states in Ising spin glasses even for
moderate system sizes. The clusters are defined to be sets of states, which are
connected in state-space by chains of zero-energy flips of spins. The technique
can also be used to estimate the sizes of such clusters. The performance of the
method is tested with respect to different system sizes and choices of
parameters. As an application the ground-state funnel structure of
two-dimensional +or- J spin glasses of systems up to size L=20 is analyzed by
calculating a huge number of ground states per realization. A T=0 entropy per
spin of s_0=0.086(4)k_B is obtained.Comment: 10 pages, 11 figures, 35 references, revte
Negative-weight percolation
We describe a percolation problem on lattices (graphs, networks), with edge
weights drawn from disorder distributions that allow for weights (or distances)
of either sign, i.e. including negative weights. We are interested whether
there are spanning paths or loops of total negative weight. This kind of
percolation problem is fundamentally different from conventional percolation
problems, e.g. it does not exhibit transitivity, hence no simple definition of
clusters, and several spanning paths/loops might coexist in the percolation
regime at the same time. Furthermore, to study this percolation problem
numerically, one has to perform a non-trivial transformation of the original
graph and apply sophisticated matching algorithms.
Using this approach, we study the corresponding percolation transitions on
large square, hexagonal and cubic lattices for two types of disorder
distributions and determine the critical exponents. The results show that
negative-weight percolation is in a different universality class compared to
conventional bond/site percolation. On the other hand, negative-weight
percolation seems to be related to the ferromagnet/spin-glass transition of
random-bond Ising systems, at least in two dimensions.Comment: v1: 4 pages, 4 figures; v2: 10 pages, 7 figures, added results, text
and reference
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