279 research outputs found
Complexity, parallel computation and statistical physics
The intuition that a long history is required for the emergence of complexity
in natural systems is formalized using the notion of depth. The depth of a
system is defined in terms of the number of parallel computational steps needed
to simulate it. Depth provides an objective, irreducible measure of history
applicable to systems of the kind studied in statistical physics. It is argued
that physical complexity cannot occur in the absence of substantial depth and
that depth is a useful proxy for physical complexity. The ideas are illustrated
for a variety of systems in statistical physics.Comment: 21 pages, 7 figure
Stationary states and energy cascades in inelastic gases
We find a general class of nontrivial stationary states in inelastic gases
where, due to dissipation, energy is transfered from large velocity scales to
small velocity scales. These steady-states exist for arbitrary collision rules
and arbitrary dimension. Their signature is a stationary velocity distribution
f(v) with an algebraic high-energy tail, f(v) ~ v^{-sigma}. The exponent sigma
is obtained analytically and it varies continuously with the spatial dimension,
the homogeneity index characterizing the collision rate, and the restitution
coefficient. We observe these stationary states in numerical simulations in
which energy is injected into the system by infrequently boosting particles to
high velocities. We propose that these states may be realized experimentally in
driven granular systems.Comment: 4 pages, 4 figure
Graphical Representations for Ising Systems in External Fields
A graphical representation based on duplication is developed that is suitable
for the study of Ising systems in external fields. Two independent replicas of
the Ising system in the same field are treated as a single four-state
(Ashkin-Teller) model. Bonds in the graphical representation connect the
Ashkin-Teller spins. For ferromagnetic systems it is proved that ordering is
characterized by percolation in this representation. The representation leads
immediately to cluster algorithms; some applications along these lines are
discussed.Comment: 13 pages amste
Dynamic and static properties of the invaded cluster algorithm
Simulations of the two-dimensional Ising and 3-state Potts models at their
critical points are performed using the invaded cluster (IC) algorithm. It is
argued that observables measured on a sub-lattice of size l should exhibit a
crossover to Swendsen-Wang (SW) behavior for l sufficiently less than the
lattice size L, and a scaling form is proposed to describe the crossover
phenomenon. It is found that the energy autocorrelation time tau(l,L) for an
l*l sub-lattice attains a maximum in the crossover region, and a dynamic
exponent z for the IC algorithm is defined according to tau_max ~ L^z.
Simulation results for the 3-state model yield z=.346(.002) which is smaller
than values of the dynamic exponent found for the SW and Wolff algorithms and
also less than the Li-Sokal bound. The results are less conclusive for the
Ising model, but it appears that z<.21 and possibly that tau_max ~ log L so
that z=0 -- similar to previous results for the SW and Wolff algorithms.Comment: 21 pages with 12 figure
Evidence of non-mean-field-like low-temperature behavior in the Edwards-Anderson spin-glass model
The three-dimensional Edwards-Anderson and mean-field Sherrington-Kirkpatrick
Ising spin glasses are studied via large-scale Monte Carlo simulations at low
temperatures, deep within the spin-glass phase. Performing a careful
statistical analysis of several thousand independent disorder realizations and
using an observable that detects peaks in the overlap distribution, we show
that the Sherrington-Kirkpatrick and Edwards-Anderson models have a distinctly
different low-temperature behavior. The structure of the spin-glass overlap
distribution for the Edwards-Anderson model suggests that its low-temperature
phase has only a single pair of pure states.Comment: 4 pages, 6 figures, 2 table
Ground states and thermal states of the random field Ising model
The random field Ising model is studied numerically at both zero and positive
temperature. Ground states are mapped out in a region of random and external
field strength. Thermal states and thermodynamic properties are obtained for
all temperatures using the the Wang-Landau algorithm. The specific heat and
susceptibility typically display sharp peaks in the critical region for large
systems and strong disorder. These sharp peaks result from large domains
flipping. For a given realization of disorder, ground states and thermal states
near the critical line are found to be strongly correlated--a concrete
manifestation of the zero temperature fixed point scenario.Comment: 5 pages, 5 figures; new material added in this versio
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