450 research outputs found
Replica Symmetry Breaking and the Renormalization Group Theory of the Weakly Disordered Ferromagnet
We study the critical properties of the weakly disordered -component
ferromagnet in terms of the renormalization group (RG) theory generalized to
take into account the replica symmetry breaking (RSB) effects coming from the
multiple local minima solutions of the mean-field equations. It is shown that
for the traditional RG flows at dimensions , which are
usually considered as describing the disorder-induced universal critical
behavior, are unstable with respect to the RSB potentials as found in spin
glasses. It is demonstrated that for a general type of the Parisi RSB
structures there exists no stable fixed points, and the RG flows lead to the
{\it strong coupling regime} at the finite scale , where
is the small parameter describing the disorder. The physical concequences
of the obtained RG solutions are discussed. In particular, we argue, that
discovered RSB strong coupling phenomena indicate on the onset of a new spin
glass type critical behaviour in the temperature interval near . Possible relevance of the considered RSB effects for
the Griffith phase is also discussed.Comment: 32 pages, Late
Effect of Random Impurities on Fluctuation-Driven First Order Transitions
We analyse the effect of quenched uncorrelated randomness coupling to the
local energy density of a model consisting of N coupled two-dimensional Ising
models. For N>2 the pure model exhibits a fluctuation-driven first order
transition, characterised by runaway renormalisation group behaviour. We show
that the addition of weak randomness acts to stabilise these flows, in such a
way that the trajectories ultimately flow back towards the pure decoupled Ising
fixed point, with the usual critical exponents alpha=0, nu=1, apart from
logarithmic corrections. We also show by examples that, in higher dimensions,
such transitions may either become continuous or remain first order in the
presence of randomness.Comment: 13 pp., LaTe
The One-dimensional KPZ Equation and the Airy Process
Our previous work on the one-dimensional KPZ equation with sharp wedge
initial data is extended to the case of the joint height statistics at n
spatial points for some common fixed time. Assuming a particular factorization,
we compute an n-point generating function and write it in terms of a Fredholm
determinant. For long times the generating function converges to a limit, which
is established to be equivalent to the standard expression of the n-point
distribution of the Airy process.Comment: 15 page
Oscillation regimes of a solid-state ring laser with active beat note stabilization : from a chaotic device to a ring laser gyroscope
We report experimental and theoretical study of a rotating diode-pumped
Nd-YAG ring laser with active beat note stabilization. Our experimental setup
is described in the usual Maxwell-Bloch formalism. We analytically derive a
stability condition and some frequency response characteristics for the
solid-state ring laser gyroscope, illustrating the important role of mode
coupling effects on the dynamics of such a device. Experimental data are
presented and compared with the theory on the basis of realistic laser
parameters, showing a very good agreement. Our results illustrate the duality
between the very rich non linear dynamics of the diode-pumped solid-state ring
laser (including chaotic behavior) and the possibility to obtain a very stable
beat note, resulting in a potentially new kind of rotation sensor
Non-perturbative phenomena in the three-dimensional random field Ising model
The systematic approach for the calculations of the non-perturbative
contributions to the free energy in the ferromagnetic phase of the random field
Ising model is developed. It is demonstrated that such contributions appear due
to localized in space instanton-like excitations. It is shown that away from
the critical region such instanton solutions are described by the set of the
mean-field saddle-point equations for the replica vector order parameter, and
these equations can be formally reduced to the only saddle-point equation of
the pure system in dimensions (D-2). In the marginal case, D=3, the
corresponding non-analytic contribution is computed explicitly. Nature of the
phase transition in the three-dimensional random field Ising model is
discussed.Comment: 12 page
The 1+1-dimensional Kardar-Parisi-Zhang equation and its universality class
We explain the exact solution of the 1+1 dimensional Kardar-Parisi-Zhang
equation with sharp wedge initial conditions. Thereby it is confirmed that the
continuum model belongs to the KPZ universality class, not only as regards to
scaling exponents but also as regards to the full probability distribution of
the height in the long time limit.Comment: Proceedings StatPhys 2
Multicritical Points and Crossover Mediating the Strong Violation of Universality: Wang-Landau Determinations in the Random-Bond Blume-Capel model
The effects of bond randomness on the phase diagram and critical behavior of
the square lattice ferromagnetic Blume-Capel model are discussed. The system is
studied in both the pure and disordered versions by the same efficient
two-stage Wang-Landau method for many values of the crystal field, restricted
here in the second-order phase transition regime of the pure model. For the
random-bond version several disorder strengths are considered. We present phase
diagram points of both pure and random versions and for a particular disorder
strength we locate the emergence of the enhancement of ferromagnetic order
observed in an earlier study in the ex-first-order regime. The critical
properties of the pure model are contrasted and compared to those of the random
model. Accepting, for the weak random version, the assumption of the double
logarithmic scenario for the specific heat we attempt to estimate the range of
universality between the pure and random-bond models. The behavior of the
strong disorder regime is also discussed and a rather complex and yet not fully
understood behavior is observed. It is pointed out that this complexity is
related to the ground-state structure of the random-bond version.Comment: 12 pages, 11 figures, submitted for publicatio
On the nature of the phase transition in the three-dimensional random field Ising model
A brief survey of the theoretical, numerical and experimental studies of the
random field Ising model during last three decades is given. Nature of the
phase transition in the three-dimensional RFIM with Gaussian random fields is
discussed. Using simple scaling arguments it is shown that if the strength of
the random fields is not too small (bigger than a certain threshold value) the
finite temperature phase transition in this system is equivalent to the
low-temperature order-disorder transition which takes place at variations of
the strength of the random fields. Detailed study of the zero-temperature phase
transition in terms of simple probabilistic arguments and modified mean-field
approach (which take into account nearest-neighbors spin-spin correlations) is
given. It is shown that if all thermally activated processes are suppressed the
ferromagnetic order parameter m(h) as the function of the strength of the
random fields becomes history dependent. In particular, the behavior of the
magnetization curves m(h) for increasing and for decreasing reveals the
hysteresis loop.Comment: 22 pages, 12 figure
Free-energy distribution of the directed polymer at high temperature
We study the directed polymer of length in a random potential with fixed
endpoints in dimension 1+1 in the continuum and on the square lattice, by
analytical and numerical methods. The universal regime of high temperature
is described, upon scaling 'time' and space (with for the discrete model) by a continuum model with
-function disorder correlation. Using the Bethe Ansatz solution for the
attractive boson problem, we obtain all positive integer moments of the
partition function. The lowest cumulants of the free energy are predicted at
small time and found in agreement with numerics. We then obtain the exact
expression at any time for the generating function of the free energy
distribution, in terms of a Fredholm determinant. At large time we find that it
crosses over to the Tracy Widom distribution (TW) which describes the fixed
infinite limit. The exact free energy distribution is obtained for any time
and compared with very recent results on growth and exclusion models.Comment: 6 pages, 3 figures large time limit corrected and convergence to
Tracy Widom established, 1 figure changed
Instantons in the Langevin dynamics: an application to spin glasses
We develop a general technique to calculate the probability of transitions
over the barriers in spin-glasses in the framework of the dynamical theory. We
use Lagrangian formulation of the instanton dynamics in which the transitions
are represented by instantons. We derive the full set of the equations that
determine the instantons but instead of solving them directly we prove that an
instanton process can be mapped into a usual process going back in time which
simplifies the problem significantly. We apply this general considerations to a
simple example of the spherical Sherrington-Kirkpatrick model and we find the
probability of the transition between the metastable states which is in
agreement with physical expectations.Comment: 18 pages, 2 figure
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