425 research outputs found
Generic Criticality in a Model of Evolution
Using Monte Carlo simulations, we show that for a certain model of biological
evolution, which is driven by non-extremal dynamics, active and absorbing
phases are separated by a critical phase. In this phase both the density of
active sites and the survival probability of spreading decay
as , where . At the critical point, which
separates the active and critical phases, , which suggests
that this point belongs to the so-called parity-conserving universality class.
The model has infinitely many absorbing states and, except for a single point,
has no conservation law.Comment: 4 pages, 3 figures, minor grammatical change
Travelling Salesman Problem with a Center
We study a travelling salesman problem where the path is optimized with a
cost function that includes its length as well as a certain measure of
its distance from the geometrical center of the graph. Using simulated
annealing (SA) we show that such a problem has a transition point that
separates two phases differing in the scaling behaviour of and , in
efficiency of SA, and in the shape of minimal paths.Comment: 4 pages, minor changes, accepted in Phys.Rev.
Novel glassy behavior in a ferromagnetic p-spin model
Recent work has suggested the existence of glassy behavior in a ferromagnetic
model with a four-spin interaction. Motivated by these findings, we have
studied the dynamics of this model using Monte Carlo simulations with
particular attention being paid to two-time quantities. We find that the system
shares many features in common with glass forming liquids. In particular, the
model exhibits: (i) a very long-lived metastable state, (ii) autocorrelation
functions that show stretched exponential relaxation, (iii) a non-equilibrium
timescale that appears to diverge at a well defined temperature, and (iv) low
temperature aging behaviour characteristic of glasses.Comment: 6 pages, 5 figure
Dimensional reduction in a model with infinitely many absorbing states
Using Monte Carlo method we study a two-dimensional model with infinitely
many absorbing states. Our estimation of the critical exponent beta=0.273(5)
suggests that the model belongs to the (1+1) rather than (2+1)
directed-percolation universality class. We also show that for a large class of
absorbing states the dynamic Monte Carlo method leads to spurious dynamical
transitions.Comment: 6 pages, 4 figures, Phys.Rev. E, Dec. 199
Poincar\'{e} cycle of a multibox Ehrenfest urn model with directed transport
We propose a generalized Ehrenfest urn model of many urns arranged
periodically along a circle. The evolution of the urn model system is governed
by a directed stochastic operation. Method for solving an -ball, -urn
problem of this model is presented. The evolution of the system is studied in
detail. We find that the average number of balls in a certain urn oscillates
several times before it reaches a stationary value. This behavior seems to be a
peculiar feature of this directed urn model. We also calculate the Poincar\'{e}
cycle, i.e., the average time interval required for the system to return to its
initial configuration. The result can be easily understood by counting the
total number of all possible microstates of the system.Comment: 10 pages revtex file with 7 eps figure
Mean Field Renormalization Group for the Boundary Magnetization of Strip Clusters
We analyze in some detail a recently proposed transfer matrix mean field
approximation which yields the exact critical point for several two dimensional
nearest neighbor Ising models. For the square lattice model we show explicitly
that this approximation yields not only the exact critical point, but also the
exact boundary magnetization of a semi--infinite Ising model, independent of
the size of the strips used. Then we develop a new mean field renormalization
group strategy based on this approximation and make connections with finite
size scaling. Applying our strategy to the quadratic Ising and three--state
Potts models we obtain results for the critical exponents which are in
excellent agreement with the exact ones. In this way we also clarify some
advantages and limitations of the mean field renormalization group approach.Comment: 16 pages (plain TeX) + 8 figures (PostScript, appended),
POLFIS-TH.XX/9
Phase transitions in nonequilibrium d-dimensional models with q absorbing states
A nonequilibrium Potts-like model with absorbing states is studied using
Monte Carlo simulations. In two dimensions and the model exhibits a
discontinuous transition. For the three-dimensional case and the model
exhibits a continuous, transition with (mean-field). Simulations are
inconclusive, however, in the two-dimensional case for . We suggest that
in this case the model is close to or at the crossing point of lines separating
three different types of phase transitions. The proposed phase diagram in the
plane is very similar to that of the equilibrium Potts model. In
addition, our simulations confirm field-theory prediction that in two
dimensions a branching-annihilating random walk model without parity
conservation belongs to the directed percolation universality class.Comment: 8 pages, figures included, accepted in Phys.Rev.
Naming Game on Adaptive Weighted Networks
We examine a naming game on an adaptive weighted network. A weight of
connection for a given pair of agents depends on their communication success
rate and determines the probability with which the agents communicate. In some
cases, depending on the parameters of the model, the preference toward
successfully communicating agents is basically negligible and the model behaves
similarly to the naming game on a complete graph. In particular, it quickly
reaches a single-language state, albeit some details of the dynamics are
different from the complete-graph version. In some other cases, the preference
toward successfully communicating agents becomes much more relevant and the
model gets trapped in a multi-language regime. In this case gradual coarsening
and extinction of languages lead to the emergence of a dominant language,
albeit with some other languages still being present. A comparison of
distribution of languages in our model and in the human population is
discussed.Comment: 22 pages, accepted in Artificial Lif
Critical phase of a magnetic hard hexagon model on triangular lattice
We introduce a magnetic hard hexagon model with two-body restrictions for
configurations of hard hexagons and investigate its critical behavior by using
Monte Carlo simulations and a finite size scaling method for discreate values
of activity. It turns out that the restrictions bring about a critical phase
which the usual hard hexagon model does not have. An upper and a lower critical
value of the discrete activity for the critical phase of the newly proposed
model are estimated as 4 and 6, respectively.Comment: 11 pages, 8 Postscript figures, uses revtex.st
Phase transition and selection in a four-species cyclic Lotka-Volterra model
We study a four species ecological system with cyclic dominance whose
individuals are distributed on a square lattice. Randomly chosen individuals
migrate to one of the neighboring sites if it is empty or invade this site if
occupied by their prey. The cyclic dominance maintains the coexistence of all
the four species if the concentration of vacant sites is lower than a threshold
value. Above the treshold, a symmetry breaking ordering occurs via growing
domains containing only two neutral species inside. These two neutral species
can protect each other from the external invaders (predators) and extend their
common territory. According to our Monte Carlo simulations the observed phase
transition is equivalent to those found in spreading models with two equivalent
absorbing states although the present model has continuous sets of absorbing
states with different portions of the two neutral species. The selection
mechanism yielding symmetric phases is related to the domain growth process
whith wide boundaries where the four species coexist.Comment: 4 pages, 5 figure
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