35 research outputs found
One Dimensional Nonequilibrium Kinetic Ising Models with Branching Annihilating Random Walk
Nonequilibrium kinetic Ising models evolving under the competing effect of
spin flips at zero temperature and nearest neighbour spin exchanges at
are investigated numerically from the point of view of a phase
transition. Branching annihilating random walk of the ferromagnetic domain
boundaries determines the steady state of the system for a range of parameters
of the model. Critical exponents obtained by simulation are found to agree,
within error, with those in Grassberger's cellular automata.Comment: 10 pages, Latex, figures upon request, SZFKI 05/9
Non-equilibrium phase transitions in one-dimensional kinetic Ising models
A family of nonequilibrium kinetic Ising models, introduced earlier, evolving
under the competing effect of spin flips at {\it zero temperature} and nearest
neighbour random spin exchanges is further investigated here. By increasing the
range of spin exchanges and/or their strength the nature of the phase
transition 'Ising-to-active' becomes of (dynamic) mean-field type and a first
order tricitical point is located at the Glauber () limit.
Corrections to mean-field theory are evaluated up to sixth order in a cluster
approximation and found to give good results concerning the phase boundary and
the critical exponent of the order parameter which is obtained as
.Comment: 15 pages, revtex file, figures available at request from
[email protected] in postscript format, submitted to J.Phys.
Three-Dimensional Ordering in Weakly Coupled Antiferromagnetic Ladders and Chains
A theoretical description is presented for low-temperature magnetic-field
induced three-dimensional (3D) ordering transitions in strongly anisotropic
quantum antiferromagnets, consisting of weakly coupled antiferromagnetic
spin-1/2 chains and ladders. First, effective continuum field theories are
derived for the one-dimensional subsystems. Then the Luttinger parameters,
which determine the low-temperature susceptibilities of the chains and ladders,
are calculated from the Bethe ansatz solution for these effective models. The
3D ordering transition line is obtained using a random phase approximation for
the weak inter-chain (inter-ladder) coupling. Finally, considering a Ginzburg
criterion, the fluctuation corrections to this approach are shown to be small.
The nature of the 3D ordered phase resembles a Bose condensate of integer-spin
magnons. It is proposed that for systems with higher spin degrees of freedom,
e.g. N-leg spin-1/2 ladders, multi-component condensates can occur at high
magnetic fields.Comment: RevTex, 18 pages with 7 figure
On the nature of different types of absorbing states
We present a comparison of three different types of Langevin equation
exhibiting absorbing states: the Langevin equation defining the Reggeon field
theory, one with multiplicative noise, and a third type in which the noise is
complex. Each one is found to describe a different underlying physical
mechanism; in particular, the nature of the different absorbing states depends
on the type of noise considered.
By studying the stationary single-site effective potential, we analyze the
impossibility of finding a reaction-diffusion model in the multiplicative noise
universality class. We also discuss some theoretical questions related to the
nature of complex noise, as for example, whether it is necessary or not to
consider a complex equation in order to describe processes as the annihilation
reaction, .Comment: 7 figures, Latex fil
Rare region effects at classical, quantum, and non-equilibrium phase transitions
Rare regions, i.e., rare large spatial disorder fluctuations, can
dramatically change the properties of a phase transition in a quenched
disordered system. In generic classical equilibrium systems, they lead to an
essential singularity, the so-called Griffiths singularity, of the free energy
in the vicinity of the phase transition. Stronger effects can be observed at
zero-temperature quantum phase transitions, at nonequilibrium phase
transitions, and in systems with correlated disorder. In some cases, rare
regions can actually completely destroy the sharp phase transition by smearing.
This topical review presents a unifying framework for rare region effects at
weakly disordered classical, quantum, and nonequilibrium phase transitions
based on the effective dimensionality of the rare regions. Explicit examples
include disordered classical Ising and Heisenberg models, insulating and
metallic random quantum magnets, and the disordered contact process.Comment: Topical review, 68 pages, 14 figures, final version as publishe
Interface depinning versus absorbing-state phase transitions
According to recent numerical results from lattice models, the critical
exponents of systems with many absorbing states and an order parameter coupled
to a non-diffusive conserved field coincide with those of the linear interface
depinning model within computational accuracy. In this paper the connection
between absorbing state phase transitions and interface pinning in quenched
disordered media is investigated. For that, we present a mapping of the
interface dynamics in a disordered medium into a Langevin equation for the
active-site density and show that a Reggeon-field-theory like description,
coupled to an additional non-diffusive conserved field, appears rather
naturally. Reciprocally, we construct a mapping from a discrete model belonging
in the absorbing state with-a-conserved-field class to a discrete interface
equation, and show how a quenched disorder is originated.
We discuss the character of the possible noise terms in both representations,
and overview the critical exponent relations. Evidence is provided that, at
least for dimensions larger that one, both universality classes are just two
different representations of the same underlying physics.Comment: 8 page
Two-Particle-Self-Consistent Approach for the Hubbard Model
Even at weak to intermediate coupling, the Hubbard model poses a formidable
challenge. In two dimensions in particular, standard methods such as the Random
Phase Approximation are no longer valid since they predict a finite temperature
antiferromagnetic phase transition prohibited by the Mermin-Wagner theorem. The
Two-Particle-Self-Consistent (TPSC) approach satisfies that theorem as well as
particle conservation, the Pauli principle, the local moment and local charge
sum rules. The self-energy formula does not assume a Migdal theorem. There is
consistency between one- and two-particle quantities. Internal accuracy checks
allow one to test the limits of validity of TPSC. Here I present a pedagogical
review of TPSC along with a short summary of existing results and two case
studies: a) the opening of a pseudogap in two dimensions when the correlation
length is larger than the thermal de Broglie wavelength, and b) the conditions
for the appearance of d-wave superconductivity in the two-dimensional Hubbard
model.Comment: Chapter in "Theoretical methods for Strongly Correlated Systems",
Edited by A. Avella and F. Mancini, Springer Verlag, (2011) 55 pages.
Misprint in Eq.(23) corrected (thanks D. Bergeron
Absorbing-state phase transitions in fixed-energy sandpiles
We study sandpile models as closed systems, with conserved energy density
playing the role of an external parameter. The critical energy density,
, marks a nonequilibrium phase transition between active and absorbing
states. Several fixed-energy sandpiles are studied in extensive simulations of
stationary and transient properties, as well as the dynamics of roughening in
an interface-height representation. Our primary goal is to identify the
universality classes of such models, in hopes of assessing the validity of two
recently proposed approaches to sandpiles: a phenomenological continuum
Langevin description with absorbing states, and a mapping to driven interface
dynamics in random media. Our results strongly suggest that there are at least
three distinct universality classes for sandpiles.Comment: 41 pages, 23 figure
One-dimensional Nonequilibrium Kinetic Ising Models with local spin-symmetry breaking: N-BARW2 transition at zero branching rate
The effects of locally broken spin symmetry are investigated in one dimensional nonequilibrium kinetic Ising systems via computer simulations and cluster mean field calculations. Beside a line of directed percolation transitions, at zero branching rate also a line of N-BARW2 transitions is revealed in the phase diagram at zero branching rate. In this way a spin model for N-BARW2 transitions is proposed for the first time