126,840 research outputs found
Critical behavior in lattice models with two symmetric absorbing state
We analyze nonequilibrium lattice models with up-down symmetry and two
absorbing states by mean-field approximations and numerical simulations in two
and three dimensions. The phase diagram displays three phases: paramagnetic,
ferromagnetic and absorbing. The transition line between the first two phases
belongs to the Ising universality class and between the last two, to the direct
percolation universality class. The two lines meet at the point describing the
voter model and the size of the ferromagnetic phase vanishes with the
distance to the voter point as , with
possible logarithm corrections in two dimensions
On the universality class of the Mott transition in two dimensions
We use the two-step density-matrix renormalization group method to elucidate
the long-standing issue of the universality class of the Mott transition in the
Hubbard model in two dimensions. We studied a spatially anisotropic
two-dimensional Hubbard model with a non-perfectly nested Fermi surface at
half-filling. We find that unlike the pure one-dimensional case where there is
no metallic phase, the quasi one-dimensional modeldisplays a genuine
metal-insulator transition at a finite value of the interaction. The critical
exponent of the correlation length is found to be . This
implies that the fermionic Mott transition, belongs to the universality class
of the 2D Ising model. The Mott insulator is the 'ordered' phase whose order
parameter is given by the density of singly occupied sites minus that of holes
and doubly occupied sites.Comment: 9 pages, 8 figure
Monte Carlo computation of correlation times of independent relaxation modes at criticality
We investigate aspects of universality of Glauber critical dynamics in two
dimensions. We compute the critical exponent and numerically corroborate
its universality for three different models in the static Ising universality
class and for five independent relaxation modes. We also present evidence for
universality of amplitude ratios, which shows that, as far as dynamic behavior
is concerned, each model in a given universality class is characterized by a
single non-universal metric factor which determines the overall time scale.
This paper also discusses in detail the variational and projection methods that
are used to compute relaxation times with high accuracy
Model independence in two dimensions and polarized cold dipolar molecules
We calculate the energy and wave functions of two particles confined to two
spatial dimensions interacting via arbitrary anisotropic potentials with
negative or zero net volume. The general rigorous analytic expressions are
given in the weak coupling limit where universality or model independence are
approached. The monopole part of anisotropic potentials is crucial in the
universal limit. We illustrate the universality with a system of two
arbitrarily polarized cold dipolar molecules in a bilayer. We discuss the
transition to universality as function of polarization and binding energy, and
compare analytic and numerical results obtained by the stochastic variational
method. The universal limit is essentially reached for experimentally
accessible strengths.Comment: 4.1 pages, 3 figures, published versio
Symmetry based determination of space-time functions in nonequilibrium growth processes
We study the space-time correlation and response functions in nonequilibrium
growth processes described by linear stochastic Langevin equations. Exploiting
exclusively the existence of space and time dependent symmetries of the
noiseless part of these equations, we derive expressions for the universal
scaling functions of two-time quantities which are found to agree with the
exact expressions obtained from the stochastic equations of motion. The
usefulness of the space-time functions is illustrated through the investigation
of two atomistic growth models, the Family model and the restricted Family
model, which are shown to belong to a unique universality class in 1+1 and in
2+1 space dimensions. This corrects earlier studies which claimed that in 2+1
dimensions the two models belong to different universality classes.Comment: 18 pages, three figures included, submitted to Phys. Rev.
Supersolid phases in the one dimensional extended soft core Bosonic Hubbard model
We present results of Quantum Monte Carlo simulations for the soft core
extended bosonic Hubbard model in one dimension exhibiting the presence of
supersolid phases similar to those recently found in two dimensions. We find
that in one and two dimensions, the insulator-supersolid transition has dynamic
critical exponent z=2 whereas the first order insulator-superfluid transition
in two dimensions is replaced by a continuous transition with z=1 in one
dimension. We present evidence that this transition is in the
Kosterlitz-Thouless universality class and discuss the mechanism behind this
difference. The simultaneous presence of two types of quasi long range order
results in two soliton-like dips in the excitation spectrum.Comment: 4 pages, 5 figure
- âŠ