34 research outputs found
Ground state structure of diluted antiferromagnets and random field systems
A method is presented for the calculation of all exact ground states of
diluted antiferromagnets and random field systems in an arbitrary range of
fields. It works by calculating all jump-fields B,\Delta where the system
changes it's ground state. For each field value all degenerated ground states
are represented by a set of (anti-) ferromagnetic clusters and a relation
between the clusters. So a complete description of the ground state structure
of these systems is possible.
Systems are investigated up to size 48^3 on the whole field-range and up to
160^3 for some particular fields. The behavior of order parameters is
investigated, the number of jumps is analyzed and the degree of degeneracy as
functions of size and fields is calculated.Comment: 11 pages, 13 figures, LaTex, submitted to Physica
Cluster-Exact Approximation of Spin Glass Groundstates
We present an algorithm which calculates groundstates of Ising spin glasses
approximately. It works by randomly selecting clusters of spins which exhibit
no frustrations. The spins which were not selected, contribute to the local
fields of the selected spins. For the spin--cluster a groundstate is exactly
calaculated by using graphtheoretical methods. The other spins remain
unchanged. This procedure is repeated many times resulting in a state with low
energy. The total time complexity of this scheme is approximately cubic. We
estimate that the groundstate energy density of the infinite system for the +/-
J model is -1.400 +/- 0.005 (2d) and -1.766 +/- 0.002 (3d). The distribution of
overlaps for selected systems is calculated in order to characterize the
algorithm.Comment: 13 pages, LaTeX (including figures in LaTeX-format
The Price of Anarchy in Transportation Networks: Efficiency and Optimality Control
Uncoordinated individuals in human society pursuing their personally optimal
strategies do not always achieve the social optimum, the most beneficial state
to the society as a whole. Instead, strategies form Nash equilibria which are
often socially suboptimal. Society, therefore, has to pay a price of anarchy
for the lack of coordination among its members. Here we assess this price of
anarchy by analyzing the travel times in road networks of several major cities.
Our simulation shows that uncoordinated drivers possibly waste a considerable
amount of their travel time. Counterintuitively,simply blocking certain streets
can partially improve the traffic conditions. We analyze various complex
networks and discuss the possibility of similar paradoxes in physics.Comment: major revisions with multicommodity; Phys. Rev. Lett., accepte
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
Ground-state behavior of the 3d +/-J random-bond Ising model
Large numbers of ground states of the three-dimensional random-bond
Ising model are calculated for sizes up to using a combination of a
genetic algorithm and Cluster-Exact Approximation. Several quantities are
calculated as function of the concentration of the antiferromagnetic bonds.
The critical concentration where the ferromagnetic order disappears is
determined using the Binder cumulant of the magnetization. A value of
is obtained. From the finite-size behavior of the Binder
cumulant and the magnetization critical exponents and
are calculated.Comment: 8 pages, 11 figures, revte
Calculation of ground states of four-dimensional +or- J Ising spin glasses
Ground states of four-dimensional (d=4) EA Ising spin glasses are calculated
for sizes up to 7x7x7x7 using a combination of a genetic algorithm and
cluster-exact approximation. The ground-state energy of the infinite system is
extrapolated as e_0=-2.095(1). The ground-state stiffness (or domain wall)
energy D is calculated. A D~L^{\Theta} behavior with \Theta=0.65(4) is found
which confirms that the d=4 model has an equilibrium spin-glass-paramagnet
transition for non-zero T_c.Comment: 5 pages, 3 figures, 31 references, revtex; update of reference
Specific-Heat Exponent of Random-Field Systems via Ground-State Calculations
Exact ground states of three-dimensional random field Ising magnets (RFIM)
with Gaussian distribution of the disorder are calculated using
graph-theoretical algorithms. Systems for different strengths h of the random
fields and sizes up to N=96^3 are considered. By numerically differentiating
the bond-energy with respect to h a specific-heat like quantity is obtained,
which does not appear to diverge at the critical point but rather exhibits a
cusp. We also consider the effect of a small uniform magnetic field, which
allows us to calculate the T=0 susceptibility. From a finite-size scaling
analysis, we obtain the critical exponents \nu=1.32(7), \alpha=-0.63(7),
\eta=0.50(3) and find that the critical strength of the random field is
h_c=2.28(1). We discuss the significance of the result that \alpha appears to
be strongly negative.Comment: 9 pages, 9 figures, 1 table, revtex revised version, slightly
extende
Imaging of hydrothermal altered zones in Wadi Al-Bana, in southern Yemen, using remote sensing techniques and very low frequency–electromagnetic data
© 2019, Saudi Society for Geosciences. Economic mineralization and hydrothermally altered zones are areas of great economic interests. This study focusses on hydrothermal altered zones of high mineralization potentials in Wadi Al-Bana, in southern Yemen. An azimuthal very low frequency–electromagnetic (AVLF-EM) data acquisition was conducted in search for mineralization in the study area. The study integrated observations from geophysical field data with others extracted from object-oriented principal component analysis (PCA) to better map and understand mineralization in the investigated area. This technique was applied to two data sets, ASTER and Landsat 8 Operational Land Imager (OLI) imagery. The results of PCA revealed high accuracy in detecting alteration minerals and for mapping zones of high concentration of these minerals. The PCA-based distribution of selected alteration zones correlated spatially with high conductivity anomalies in the subsurface that were detected by VLF measurements. Finally, a GIS model was built and successfully utilized to categorize the resulted altered zones, into three levels. [Figure not available: see fulltext.]