17,467 research outputs found
Phase Diagrams and Crossover in Spatially Anisotropic d=3 Ising, XY Magnetic and Percolation Systems: Exact Renormalization-Group Solutions of Hierarchical Models
Hierarchical lattices that constitute spatially anisotropic systems are
introduced. These lattices provide exact solutions for hierarchical models and,
simultaneously, approximate solutions for uniaxially or fully anisotropic d=3
physical models. The global phase diagrams, with d=2 and d=1 to d=3 crossovers,
are obtained for Ising, XY magnetic models and percolation systems, including
crossovers from algebraic order to true long-range order.Comment: 7 pages, 12 figures. Corrected typos, added publication informatio
Zero-Temperature Complex Replica Zeros of the Ising Spin Glass on Mean-Field Systems and Beyond
Zeros of the moment of the partition function with respect
to complex are investigated in the zero temperature limit , keeping . We numerically investigate
the zeros of the Ising spin glass models on several Cayley trees and
hierarchical lattices and compare those results. In both lattices, the
calculations are carried out with feasible computational costs by using
recursion relations originated from the structures of those lattices. The
results for Cayley trees show that a sequence of the zeros approaches the real
axis of implying that a certain type of analyticity breaking actually
occurs, although it is irrelevant for any known replica symmetry breaking. The
result of hierarchical lattices also shows the presence of analyticity
breaking, even in the two dimensional case in which there is no
finite-temperature spin-glass transition, which implies the existence of the
zero-temperature phase transition in the system. A notable tendency of
hierarchical lattices is that the zeros spread in a wide region of the complex
plane in comparison with the case of Cayley trees, which may reflect the
difference between the mean-field and finite-dimensional systems.Comment: 4 pages, 4 figure
Self-similarity, small-world, scale-free scaling, disassortativity, and robustness in hierarchical lattices
In this paper, firstly, we study analytically the topological features of a
family of hierarchical lattices (HLs) from the view point of complex networks.
We derive some basic properties of HLs controlled by a parameter . Our
results show that scale-free networks are not always small-world, and support
the conjecture that self-similar scale-free networks are not assortative.
Secondly, we define a deterministic family of graphs called small-world
hierarchical lattices (SWHLs). Our construction preserves the structure of
hierarchical lattices, while the small-world phenomenon arises. Finally, the
dynamical processes of intentional attacks and collective synchronization are
studied and the comparisons between HLs and Barab{\'asi}-Albert (BA) networks
as well as SWHLs are shown. We show that degree distribution of scale-free
networks does not suffice to characterize their synchronizability, and that
networks with smaller average path length are not always easier to synchronize.Comment: 26 pages, 8 figure
Lower-Critical Spin-Glass Dimension from 23 Sequenced Hierarchical Models
The lower-critical dimension for the existence of the Ising spin-glass phase
is calculated, numerically exactly, as for a family of
hierarchical lattices, from an essentially exact (correlation coefficent ) near-linear fit to 23 different diminishing fractional dimensions.
To obtain this result, the phase transition temperature between the disordered
and spin-glass phases, the corresponding critical exponent , and the
runaway exponent of the spin-glass phase are calculated for consecutive
hierarchical lattices as dimension is lowered.Comment: 5 pages, 2 figures, 1 tabl
Potts models on hierarchical lattices and Renormalization Group dynamics
We prove that the generator of the renormalization group of Potts models on
hierarchical lattices can be represented by a rational map acting on a
finite-dimensional product of complex projective spaces. In this framework we
can also consider models with an applied external magnetic field and
multiple-spin interactions. We use recent results regarding iteration of
rational maps in several complex variables to show that, for some class of
hierarchical lattices, Lee-Yang and Fisher zeros belong to the unstable set of
the renormalization map.Comment: 21 pages, 7 figures; v3 revised, some issues correcte
Universality and Crossover of Directed Polymers and Growing Surfaces
We study KPZ surfaces on Euclidean lattices and directed polymers on
hierarchical lattices subject to different distributions of disorder, showing
that universality holds, at odds with recent results on Euclidean lattices.
Moreover, we find the presence of a slow (power-law) crossover toward the
universal values of the exponents and verify that the exponent governing such
crossover is universal too. In the limit of a 1+epsilon dimensional system we
obtain both numerically and analytically that the crossover exponent is 1/2.Comment: LateX file + 5 .eps figures; to appear on Phys. Rev. Let
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Direct Extrusion Freeforming of Ceramic Pastes
Microextrusion freeforming of ceramic lattices from high solids ceramic pastes provides
multi-scale hierarchical void structures with the advantages of low shrinkage stress and high
sintered density. Alumina lattices were directly fabricated using 80-500 Pm diameter filaments.
We report here on the implementation of design and fabrication of these scaffolds for band gap
materials and micro fluidic devices.Mechanical Engineerin
Reduction of Spin Glasses applied to the Migdal-Kadanoff Hierarchical Lattice
A reduction procedure to obtain ground states of spin glasses on sparse
graphs is developed and tested on the hierarchical lattice associated with the
Migdal-Kadanoff approximation for low-dimensional lattices. While more
generally applicable, these rules here lead to a complete reduction of the
lattice. The stiffness exponent governing the scaling of the defect energy
with system size , , is obtained as
by reducing the equivalent of lattices up to in
, and as for up to in . The reduction
rules allow the exact determination of the ground state energy, entropy, and
also provide an approximation to the overlap distribution. With these methods,
some well-know and some new features of diluted hierarchical lattices are
calculated.Comment: 7 pages, RevTex, 6 figures (postscript), added results for d=4, some
corrections; final version, as to appear in EPJ
Evolutionary prisoner's dilemma game on hierarchical lattices
An evolutionary prisoner's dilemma (PD) game is studied with players located
on a hierarchical structure of layered square lattices. The players can follow
two strategies [D (defector) and C (cooperator)] and their income comes from PD
games with the ``neighbors.'' The adoption of one of the neighboring strategies
is allowed with a probability dependent on the payoff difference. Monte Carlo
simulations are performed to study how the measure of cooperation is affected
by the number of hierarchical levels (Q) and by the temptation to defect.
According to the simulations the highest frequency of cooperation can be
observed at the top level if the number of hierarchical levels is low (Q<4).
For larger Q, however, the highest frequency of cooperators occurs in the
middle layers. The four-level hierarchical structure provides the highest
average (total) income for the whole community.Comment: appendix adde
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