12,114 research outputs found

### A Finite Size Scaling Study of Lattice Models in the three-dimensional Ising Universality Class

We simulate the spin-1/2 Ising model and the Blume-Capel model at various
values of the parameter D on the simple cubic lattice. We perform a finite size
scaling study of lattices of a linear size up to L=360 to obtain accurate
estimates for critical exponents. We focus on values of D, where the amplitudes
of leading corrections are small. Furthermore we employ improved observables
that have a small amplitude of the leading correction. We obtain
nu=0.63002(10), eta=0.03627(10) and omega=0.832(6). We compare our results with
those obtained from previous Monte Carlo simulations and high temperature
series expansions of lattice models, by using field theoretic methods and
experiments.Comment: 25 pages, 6 figures, typos corrected, references added, conclusions
extende

### Mott Transition in Quasi-One-Dimensional Systems

We report the application of the density-matrix renormalization group method
to a spatially anisotropic two-dimensional Hubbard model at half-filling. We
find a deconfinement transition induced by the transverse hopping parameter
$t_y$ from an insulator to a metal. Therefore, if $t_y$ is fixed in the
metallic phase, increasing the interaction $U$ leads to a metal-to-insulator
transition at a finite critical $U$. This is in contrast to the weak-coupling
Hartree-Fock theory which predicts a nesting induced antiferromagnetic
insulator for any $U>0$.Comment: 4 pages, 3 figure

### 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 $\nu \approx 1.0$. 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

### Universal amplitude ratios in the 3D Ising Universality Class

We compute a number of universal amplitude ratios in the three-dimensional
Ising universality class. To this end, we perform Monte Carlo simulations of
the improved Blume-Capel model on the simple cubic lattice. For example, we
obtain A_+/A_-=0.536(2) and C_+/C_-=4.713(7), where A_+- and C_+- are the
amplitudes of the specific heat and the magnetic susceptibility, respectively.
The subscripts + and - indicate the high and the low temperature phase,
respectively. We compare our results with those obtained from previous Monte
Carlo simulations, high and low temperature series expansions, field theoretic
methods and experiments.Comment: 18 pages, two figures, typos corrected, discussion on finite size
corrections extende

### Solving the puzzle of an unconventional phase transition for a 2d dimerized quantum Heisenberg model

Motivated by the indication of a new critical theory for the spin-1/2
Heisenberg model with a spatially staggered anisotropy on the square lattice as
suggested in \cite{Wenzel08}, we re-investigate the phase transition of this
model induced by dimerization using first principle Monte Carlo simulations. We
focus on studying the finite-size scaling of $\rho_{s1} 2L$ and $\rho_{s2} 2L$,
where $L$ stands for the spatial box size used in the simulations and
$\rho_{si}$ with $i \in \{1,2\}$ is the spin-stiffness in the $i$-direction.
Remarkably, while we do observe a large correction to scaling for the
observable $\rho_{s1}2L$ as proposed in \cite{Fritz11}, the data for
$\rho_{s2}2L$ exhibit a good scaling behavior without any indication of a large
correction. As a consequence, we are able to obtain a numerical value for the
critical exponent $\nu$ which is consistent with the known O(3) result with
moderate computational effort. Specifically, the numerical value of $\nu$ we
determine by fitting the data points of $\rho_{s2}2L$ to their expected scaling
form is given by $\nu=0.7120(16)$, which agrees quantitatively with the most
accurate known Monte Carlo O(3) result $\nu = 0.7112(5)$. Finally, while we can
also obtain a result of $\nu$ from the observable second Binder ratio $Q_2$
which is consistent with $\nu=0.7112(5)$, the uncertainty of $\nu$ calculated
from $Q_2$ is more than twice as large as that of $\nu$ determined from
$\rho_{s2}2L$.Comment: 7 figures, 1 table; brief repor

### Evidence for O(2) universality at the finite temperature transition for lattice QCD with 2 flavours of massless staggered quarks

We simulate lattice QCD with 2 flavours of massless quarks on lattices of
temporal extent N_t=8, to study the finite temperature transition from hadronic
matter to a quark-gluon plasma. A modified action which incorporates an
irrelevant chiral 4-fermion interaction is used, which allows simulations at
zero quark mass. We obtain excellent fits of the chiral condensates to the
magnetizations of a 3-dimensional O(2) spin model on lattices small enough to
model the finite size effects. This gives predictions for correlation lengths
and chiral susceptibilities from the corresponding spin-model quantities. These
are in good agreement with our measurements over the relevant range of
parameters. Binder cumulants are measured, but the errors are too large to draw
definite conclusions. From the properties of the O(2) spin model on the
relatively small lattices with which we fit our `data', we can see why earlier
attempts to fit staggered lattice data to leading-order infinite-volume scaling
functions, as well as finite size scaling studies, failed and led to erroneous
conclusions.Comment: 27 pages, Latex with 10 postscript figures. Some of the discussions
have been expanded to satisfy a referee. Typographical errors were correcte

### Interplay between temperature and trap effects in one-dimensional lattice systems of bosonic particles

We investigate the interplay of temperature and trap effects in cold particle
systems at their quantum critical regime, such as cold bosonic atoms in optical
lattices at the transitions between Mott-insulator and superfluid phases. The
theoretical framework is provided by the one-dimensional Bose-Hubbard model in
the presence of an external trapping potential, and the trap-size scaling
theory describing the large trap-size behavior at a quantum critical point. We
present numerical results for the low-temperature behavior of the particle
density and the density-density correlation function at the Mott transitions,
and within the gapless superfluid phase.Comment: 9 page

### Slow dynamics at the smeared phase transition of randomly layered magnets

We investigate a model for randomly layered magnets, viz. a three-dimensional
Ising model with planar defects. The magnetic phase transition in this system
is smeared because static long-range order can develop on isolated rare spatial
regions. Here, we report large-scale kinetic Monte Carlo simulations of the
dynamical behavior close to the smeared phase transition which we characterize
by the spin (time) autocorrelation function. In the paramagnetic phase, its
behavior is dominated by Griffiths effects similar to those in magnets with
point defects. In the tail region of the smeared transition the dynamics is
even slower: the autocorrelation function decays like a stretched exponential
at intermediate times before approaching the exponentially small asymptotic
value following a power law at late times. Our Monte-Carlo results are in good
agreement with recent theoretical predictions based on optimal fluctuation
theory.Comment: 7 pages, 6 eps figures, final version as publishe

### Phase structure of lattice QCD with two flavors of Wilson quarks at finite temperature and chemical potential

We present results for phase structure of lattice QCD with two degenerate
flavors ($N_f=2$) of Wilson quarks at finite temperature $T$ and small baryon
chemical potential $\mu_B$. Using the imaginary chemical potential for which
the fermion determinant is positive, we perform simulations at points where the
ratios of pseudo-scalar meson mass to the vector meson mass $m_\pi/m_\rho$ are
between $0.943(3)$ and $0.899(4)$ as well as in the quenched limit. By analytic
continuation to real quark chemical potential $\mu$, we obtain the transition
temperature as a function of small $\mu_B$. We attempt to determine the nature
of transition at imaginary chemical potential by histogram, MC history, and
finite size scaling. In the infinite heavy quark limit, the transition is of
first order. At intermediate values of quark mass $m_q$ corresponding to the
ratio of $m_\pi/m_\rho$ in the range from $0.943(3)$ to $0.899(4)$ at
$a\mu_I=0.24$, the MC simulations show absence of phase transition.Comment: 10 pages, 17 figures;16 figures;9 pages,10 figures;10 pages,11
figure

### Composition-tuned smeared phase transitions

Phase transitions in random systems are smeared if individual spatial regions
can order independently of the bulk system. In this paper, we study such
smeared phase transitions (both classical and quantum) in substitutional alloys
A$_{1-x}$B$_x$ that can be tuned from an ordered phase at composition $x=0$ to
a disordered phase at $x=1$. We show that the ordered phase develops a
pronounced tail that extends over all compositions $x<1$. Using optimal
fluctuation theory, we derive the composition dependence of the order parameter
and other quantities in the tail of the smeared phase transition. We also
compare our results to computer simulations of a toy model, and we discuss
experiments.Comment: 6 pages, 4 eps figures included, final version as publishe

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