139 research outputs found
Spontaneous magnetization of the Ising model on the Sierpinski carpet fractal, a rigorous result
We give a rigorous proof of the existence of spontaneous magnetization at
finite temperature for the Ising spin model defined on the Sierpinski carpet
fractal. The theorem is inspired by the classical Peierls argument for the two
dimensional lattice. Therefore, this exact result proves the existence of
spontaneous magnetization for the Ising model in low dimensional structures,
i.e. structures with dimension smaller than 2.Comment: 14 pages, 8 figure
Multifractals of Normalized First Passage Time in Sierpinski Gasket
The multifractal behavior of the normalized first passage time is
investigated on the two dimensional Sierpinski gasket with both absorbing and
reflecting barriers. The normalized first passage time for Sinai model and the
logistic model to arrive at the absorbing barrier after starting from an
arbitrary site, especially obtained by the calculation via the Monte Carlo
simulation, is discussed numerically. The generalized dimension and the
spectrum are also estimated from the distribution of the normalized first
passage time, and compared with the results on the finitely square lattice.Comment: 10 pages, Latex, with 3 figures and 1 table. to be published in J.
Phys. Soc. Jpn. Vol.67(1998
Disorder, Order, and Domain Wall Roughening in the 2d Random Field Ising Model
Ground states and domain walls are investigated with exact combinatorial
optimization in two-dimensional random field Ising magnets. The ground states
break into domains above a length scale that depends exponentially on the
random field strength squared. For weak disorder, this paramagnetic structure
has remnant long-range order of the percolation type. The domain walls are
super-rough in ordered systems with a roughness exponent close to 6/5.
The interfaces exhibit rare fluctuations and multiscaling reminiscent of some
models of kinetic roughening and hydrodynamic turbulence.Comment: to be published in Phys.Rev.E/Rapid.Com
On the nature of the phase transition in the three-dimensional random field Ising model
A brief survey of the theoretical, numerical and experimental studies of the
random field Ising model during last three decades is given. Nature of the
phase transition in the three-dimensional RFIM with Gaussian random fields is
discussed. Using simple scaling arguments it is shown that if the strength of
the random fields is not too small (bigger than a certain threshold value) the
finite temperature phase transition in this system is equivalent to the
low-temperature order-disorder transition which takes place at variations of
the strength of the random fields. Detailed study of the zero-temperature phase
transition in terms of simple probabilistic arguments and modified mean-field
approach (which take into account nearest-neighbors spin-spin correlations) is
given. It is shown that if all thermally activated processes are suppressed the
ferromagnetic order parameter m(h) as the function of the strength of the
random fields becomes history dependent. In particular, the behavior of the
magnetization curves m(h) for increasing and for decreasing reveals the
hysteresis loop.Comment: 22 pages, 12 figure
Ground state numerical study of the three-dimensional random field Ising model
The random field Ising model in three dimensions with Gaussian random fields
is studied at zero temperature for system sizes up to 60^3. For each
realization of the normalized random fields, the strength of the random field,
Delta and a uniform external, H is adjusted to find the finite-size critical
point. The finite-size critical point is identified as the point in the H-Delta
plane where three degenerate ground states have the largest discontinuities in
the magnetization. The discontinuities in the magnetization and bond energy
between these ground states are used to calculate the magnetization and
specific heat critical exponents and both exponents are found to be near zero.Comment: 10 pages, 6 figures; new references and small changes to tex
Percolation in three-dimensional random field Ising magnets
The structure of the three-dimensional random field Ising magnet is studied
by ground state calculations. We investigate the percolation of the minority
spin orientation in the paramagnetic phase above the bulk phase transition,
located at [Delta/J]_c ~= 2.27, where Delta is the standard deviation of the
Gaussian random fields (J=1). With an external field H there is a disorder
strength dependent critical field +/- H_c(Delta) for the down (or up) spin
spanning. The percolation transition is in the standard percolation
universality class. H_c ~ (Delta - Delta_p)^{delta}, where Delta_p = 2.43 +/-
0.01 and delta = 1.31 +/- 0.03, implying a critical line for Delta_c < Delta <=
Delta_p. When, with zero external field, Delta is decreased from a large value
there is a transition from the simultaneous up and down spin spanning, with
probability Pi_{uparrow downarrow} = 1.00 to Pi_{uparrow downarrow} = 0. This
is located at Delta = 2.32 +/- 0.01, i.e., above Delta_c. The spanning cluster
has the fractal dimension of standard percolation D_f = 2.53 at H = H_c(Delta).
We provide evidence that this is asymptotically true even at H=0 for Delta_c <
Delta <= Delta_p beyond a crossover scale that diverges as Delta_c is
approached from above. Percolation implies extra finite size effects in the
ground states of the 3D RFIM.Comment: replaced with version to appear in Physical Review
The Computational Complexity of Generating Random Fractals
In this paper we examine a number of models that generate random fractals.
The models are studied using the tools of computational complexity theory from
the perspective of parallel computation. Diffusion limited aggregation and
several widely used algorithms for equilibrating the Ising model are shown to
be highly sequential; it is unlikely they can be simulated efficiently in
parallel. This is in contrast to Mandelbrot percolation that can be simulated
in constant parallel time. Our research helps shed light on the intrinsic
complexity of these models relative to each other and to different growth
processes that have been recently studied using complexity theory. In addition,
the results may serve as a guide to simulation physics.Comment: 28 pages, LATEX, 8 Postscript figures available from
[email protected]
The Origins of the Circumgalactic Medium in the FIRE Simulations
We use a particle tracking analysis to study the origins of the
circumgalactic medium (CGM), separating it into (1) accretion from the
intergalactic medium (IGM), (2) wind from the central galaxy, and (3) gas
ejected from other galaxies. Our sample consists of 21 FIRE-2 simulations,
spanning the halo mass range log(Mh/Msun) ~ 10-12 , and we focus on z=0.25 and
z=2. Owing to strong stellar feedback, only ~L* halos retain a baryon mass
>~50% of their cosmic budget. Metals are more efficiently retained by halos,
with a retention fraction >~50%. Across all masses and redshifts analyzed >~60%
of the CGM mass originates as IGM accretion (some of which is associated with
infalling halos). Overall, the second most important contribution is wind from
the central galaxy, though gas ejected or stripped from satellites can
contribute a comparable mass in ~L* halos. Gas can persist in the CGM for
billions of years, resulting in well-mixed halo gas. Sight lines through the
CGM are therefore likely to intersect gas of multiple origins. For low-redshift
~L* halos, cool gas (T<10^4.7 K) is distributed on average preferentially along
the galaxy plane, however with strong halo-to-halo variability. The metallicity
of IGM accretion is systematically lower than the metallicity of winds
(typically by >~1 dex), although CGM and IGM metallicities depend significantly
on the treatment of subgrid metal diffusion. Our results highlight the multiple
physical mechanisms that contribute to the CGM and will inform observational
efforts to develop a cohesive picture.Comment: 23 pages, 22 figures. Minor revisions from previous version. Online
interactive visualizations available at zhafen.github.io/CGM-origins and
zhafen.github.io/CGM-origins-pathline
An introduction to Graph Data Management
A graph database is a database where the data structures for the schema
and/or instances are modeled as a (labeled)(directed) graph or generalizations
of it, and where querying is expressed by graph-oriented operations and type
constructors. In this article we present the basic notions of graph databases,
give an historical overview of its main development, and study the main current
systems that implement them
G-CORE a core for future graph query languages
We report on a community effort between industry and academia to shape the future of graph query languages. We argue that existing graph database management systems should consider supporting a query language with two key characteristics. First, it should be composable, meaning, that graphs are the input and the output of queries. Second, the graph query language should treat paths as first-class citizens. Our result is G-CORE, a powerful graph query language design that fulfills these goals, and strikes a careful balance between path query expressivity and evaluation complexity
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