36 research outputs found
Boundary field induced first-order transition in the 2D Ising model: numerical study
In a recent paper, Clusel and Fortin [J. Phys. A.: Math. Gen. 39 (2006) 995]
presented an analytical study of a first-order transition induced by an
inhomogeneous boundary magnetic field in the two-dimensional Ising model. They
identified the transition that separates the regime where the interface is
localized near the boundary from the one where it is propagating inside the
bulk. Inspired by these results, we measured the interface tension by using
multimagnetic simulations combined with parallel tempering to determine the
phase transition and the location of the interface. Our results are in very
good agreement with the theoretical predictions. Furthermore, we studied the
spin-spin correlation function for which no analytical results are available.Comment: 12 pages, 7 figures, 2 table
Dephasing due to nonstationary 1/f noise
Motivated by recent experiments with Josephson qubits we propose a new
phenomenological model for 1/f noise due to collective excitations of
interacting defects in the qubit's environment. At very low temperatures the
effective dynamics of these collective modes are very slow leading to
pronounced non-Gaussian features and nonstationarity of the noise. We analyze
the influence of this noise on the dynamics of a qubit in various regimes and
at different operation points. Remarkable predictions are absolute time
dependences of a critical coupling and of dephasing in the strong coupling
regime.Comment: 4 pages, 2 figures, to be published in the proceedings of the Vth
Rencontres de Moriond in Mesoscopic Physic
Second-order critical lines of spin-S Ising models in a splitting field with Grassmann techniques
We propose a method to study the second-order critical lines of classical
spin- Ising models on two-dimensional lattices in a crystal or splitting
field, using an exact expression for the bare mass of the underlying field
theory. Introducing a set of anticommuting variables to represent the partition
function, we derive an exact and compact expression for the bare mass of the
model including all local multi-fermions interactions. By extension of the
Ising and Blume-Capel models, we extract the free energy singularities in the
low momentum limit corresponding to a vanishing bare mass. The loci of these
singularities define the critical lines depending on the spin S, in good
agreement with previous numerical estimations. This scheme appears to be
general enough to be applied in a variety of classical Hamiltonians
Dephasing by a nonstationary classical intermittent noise
We consider a new phenomenological model for a classical
intermittent noise and study its effects on the dephasing of a two-level
system. Within this model, the evolution of the relative phase between the
states is described as a continuous time random walk (CTRW). Using
renewal theory, we find exact expressions for the dephasing factor and identify
the physically relevant various regimes in terms of the coupling to the noise.
In particular, we point out the consequences of the non-stationarity and
pronounced non-Gaussian features of this noise, including some new anomalous
and aging dephasing scenarii.Comment: Submitted to Phys. Rev.
Origin of the approximate universality of distributions in equilibrium correlated systems
We propose an interpretation of previous experimental and numerical
experiments, showing that for a large class of systems, distributions of global
quantities are similar to a distribution originally obtained for the
magnetization in the 2D-XY model . This approach, developed for the Ising
model, is based on previous numerical observations. We obtain an effective
action using a perturbative method, which successfully describes the order
parameter fluctuations near the phase transition. This leads to a direct link
between the D-dimensional Ising model and the XY model in the same dimension,
which appears to be a generic feature of many equilibrium critical systems and
which is at the heart of the above observations.Comment: To appear in Europhysics Letter
Nonstationary dephasing of two level systems
We investigate the influence of nonstationary 1/f^mu noise, produced by
interacting defects, on a quantum two-level system. Adopting a simple
phenomenological model for this noise we describe exactly the corresponding
dephasing in various regimes. The nonstationarity and pronounced non-Gaussian
features of this noise induce new anomalous dephasing scenarii. Beyond a
history-dependent critical coupling strength the dephasing time exhibits a
strong dependence on the age of the noise and the decay of coherence is not
exponential
Dephasing due to nonstationary 1/f noise
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Temperature dependent fluctuations in the two-dimensional XY model
We present a detailed investigation of the probability density function (PDF)
of order parameter fluctuations in the finite two-dimensional XY (2dXY) model.
In the low temperature critical phase of this model, the PDF approaches a
universal non-Gaussian limit distribution in the limit T-->0. Our analysis
resolves the question of temperature dependence of the PDF in this regime, for
which conflicting results have been reported. We show analytically that a weak
temperature dependence results from the inclusion of multiple loop graphs in a
previously-derived graphical expansion. This is confirmed by numerical
simulations on two controlled approximations to the 2dXY model: the Harmonic
and ``Harmonic XY'' models. The Harmonic model has no
Kosterlitz-Thouless-Berezinskii (KTB) transition and the PDF becomes
progressively less skewed with increasing temperature until it closely
approximates a Gaussian function above T ~ 4\pi. Near to that temperature we
find some evidence of a phase transition, although our observations appear to
exclude a thermodynamic singularity.Comment: 15 pages, 5 figures and 1 tabl
Alternative description of the 2D Blume-Capel model using Grassmann algebra
We use Grassmann algebra to study the phase transition in the two-dimensional
ferromagnetic Blume-Capel model from a fermionic point of view. This model
presents a phase diagram with a second order critical line which becomes first
order through a tricritical point, and was used to model the phase transition
in specific magnetic materials and liquid mixtures of He-He. In
particular, we are able to map the spin-1 system of the BC model onto an
effective fermionic action from which we obtain the exact mass of the theory,
the condition of vanishing mass defines the critical line. This effective
action is actually an extension of the free fermion Ising action with an
additional quartic interaction term. The effect of this term is merely to
render the excitation spectrum of the fermions unstable at the tricritical
point. The results are compared with recent numerical Monte-Carlo simulations.Comment: 32 pages, 2 figures
Nature of the global fluctuations in the spherical model at criticality
We study the universal nature of global fluctuations in the critical regime
of the spherical model by evaluating the exact distribution of the
magnetization and its absolute value in the thermodynamical limit, in the
presence of a conjugate field. We show that the probability distribution
function for this model is described by non-Gaussian asymptotics and
non-symmetric characteristics which depend on the dimension of the system
2<d<4. Relation with extreme statistics of independent wavelength modes is
discussed.Comment: 22 pages, 8 figures; 05.70.Jk, 05.40.-a, 05.50.+q, 68.35.R