480 research outputs found
Multiplicity of species in some replicative systems
In an attempt to explain the uniqueness of the coding mechanism of living
cells as contrasted with multi-species structure of ecosystems we examine two
models of individuals with some replicative properties. In the first model the
system generically remains in a multi-species state. Even though for some of
these species the replicative probability is very high, they are unable to
invade the system. In the second model, in which the death rate depends on the
type of the species, the system relatively quickly reaches a single-species
state and fluctuations might at most bring it to yet another single-species
state.Comment: 9 pages, 7 figures, submitted to Phys.Rev.
Novel criticality in a model with absorbing states
We study a one-dimensional model which undergoes a transition between an
active and an absorbing phase. Monte Carlo simulations supported by some
additional arguments prompted as to predict the exact location of the critical
point and critical exponents in this model. The exponents and
follows from random-walk-type arguments. The exponents are found to be non-universal and encoded in the singular part of
reactivation probability, as recently discussed by H. Hinrichsen
(cond-mat/0008179). A related model with quenched randomness is also studied.Comment: 5 pages, 5 figures, generalized version with the continuously
changing exponent bet
Criticality of natural absorbing states
We study a recently introduced ladder model which undergoes a transition
between an active and an infinitely degenerate absorbing phase. In some cases
the critical behaviour of the model is the same as that of the branching
annihilating random walk with species both with and without hard-core
interaction. We show that certain static characteristics of the so-called
natural absorbing states develop power law singularities which signal the
approach of the critical point. These results are also explained using random
walk arguments. In addition to that we show that when dynamics of our model is
considered as a minimum finding procedure, it has the best efficiency very
close to the critical point.Comment: 6 page
Crystallization of a supercooled liquid and of a glass - Ising model approach
Using Monte Carlo simulations we study crystallization in the
three-dimensional Ising model with four-spin interaction. We monitor the
morphology of crystals which grow after placing crystallization seeds in a
supercooled liquid. Defects in such crystals constitute an intricate and very
stable network which separate various domains by tensionless domain walls. We
also show that the crystallization which occurs during the continuous heating
of the glassy phase takes place at a heating-rate dependent temperature.Comment: 7 page
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
The Gonihedric Ising Model and Glassiness
The Gonihedric 3D Ising model is a lattice spin model in which planar Peierls
boundaries between + and - spins can be created at zero energy cost. Instead of
weighting the area of Peierls boundaries as the case for the usual 3D Ising
model with nearest neighbour interactions, the edges, or "bends" in an
interface are weighted, a concept which is related to the intrinsic curvature
of the boundaries in the continuum.
In these notes we follow a roughly chronological order by first reviewing the
background to the formulation of the model, before moving on to the elucidation
of the equilibrium phase diagram by various means and then to investigation of
the non-equilibrium, glassy behaviour of the model.Comment: To appear as Chapter 7 in Rugged Free-Energy Landscapes - An
Introduction, Springer Lecture Notes in Physics, 736, ed. W. Janke, (2008
Glassy transition and metastability in four-spin Ising model
Using Monte Carlo simulations we show that the three-dimensional Ising model
with four-spin (plaquette) interactions has some characteristic glassy
features. The model dynamically generates diverging energy barriers, which give
rise to slow dynamics at low temperature. Moreover, in a certain temperature
range the model possesses a metastable (supercooled liquid) phase, which is
presumably supported by certain entropy barriers. Although extremely strong,
metastability in our model is only a finite-size effect and sufficiently large
droplets of stable phase divert evolution of the system toward the stable
phase. Thus, the glassy transitions in this model is a dynamic transition,
preceded by a pronounced peak in the specific heat.Comment: extensively revised, with further simulations of metastability
properties, response to referees tactfully remove
Slow dynamics in the 3--D gonihedric model
We study dynamical aspects of three--dimensional gonihedric spins by using
Monte--Carlo methods. The interest of this family of models (parametrized by
one self-avoidance parameter ) lies in their capability to show
remarkably slow dynamics and seemingly glassy behaviour below a certain
temperature without the need of introducing disorder of any kind. We
consider first a hamiltonian that takes into account only a four--spin term
(), where a first order phase transition is well established. By
studying the relaxation properties at low temperatures we confirm that the
model exhibits two distinct regimes. For , with long lived
metastability and a supercooled phase, the approach to equilibrium is well
described by a stretched exponential. For the dynamics appears to be
logarithmic. We provide an accurate determination of . We also determine
the evolution of particularly long lived configurations. Next, we consider the
case , where the plaquette term is absent and the gonihedric action
consists in a ferromagnetic Ising with fine-tuned next-to-nearest neighbour
interactions. This model exhibits a second order phase transition. The
consideration of the relaxation time for configurations in the cold phase
reveals the presence of slow dynamics and glassy behaviour for any .
Type II aging features are exhibited by this model.Comment: 13 pages, 12 figure
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