1,055 research outputs found
Generalized Heisenberg algebras and k-generalized Fibonacci numbers
It is shown how some of the recent results of de Souza et al. [1] can be
generalized to describe Hamiltonians whose eigenvalues are given as
k-generalized Fibonacci numbers. Here k is an arbitrary integer and the cases
considered by de Souza et al. corespond to k=2.Comment: 8 page
Extended surface disorder in the quantum Ising chain
We consider random extended surface perturbations in the transverse field
Ising model decaying as a power of the distance from the surface towards a pure
bulk system. The decay may be linked either to the evolution of the couplings
or to their probabilities. Using scaling arguments, we develop a
relevance-irrelevance criterion for such perturbations. We study the
probability distribution of the surface magnetization, its average and typical
critical behaviour for marginal and relevant perturbations. According to
analytical results, the surface magnetization follows a log-normal distribution
and both the average and typical critical behaviours are characterized by
power-law singularities with continuously varying exponents in the marginal
case and essential singularities in the relevant case. For enhanced average
local couplings, the transition becomes first order with a nonvanishing
critical surface magnetization. This occurs above a positive threshold value of
the perturbation amplitude in the marginal case.Comment: 15 pages, 10 figures, Plain TeX. J. Phys. A (accepted
Conformal off-diagonal boundary density profiles on a semi-infinite strip
The off-diagonal profile phi(v) associated with a local operator (order
parameter or energy density) close to the boundary of a semi-infinite strip
with width L is obtained at criticality using conformal methods. It involves
the surface exponent x_phi^s and displays a simple universal behaviour which
crosses over from surface finite-size scaling when v/L is held constant to
corner finite-size scaling when v/L -> 0.Comment: 5 pages, 1 figure, IOP macros and eps
Radial Fredholm perturbation in the two-dimensional Ising model and gap-exponent relation
We consider concentric circular defects in the two-dimensional Ising model,
which are distributed according to a generalized Fredholm sequence, i. e. at
exponentially increasing radii. This type of aperiodicity does not change the
bulk critical behaviour but introduces a marginal extended perturbation. The
critical exponent of the local magnetization is obtained through finite-size
scaling, using a corner transfer matrix approach in the extreme anisotropic
limit. It varies continuously with the amplitude of the modulation and is
closely related to the magnetic exponent of the radial Hilhorst-van Leeuwen
model. Through a conformal mapping of the system onto a strip, the gap-exponent
relation is shown to remain valid for such an aperiodic defect.Comment: 12 pages, TeX file + 4 figures, epsf neede
Vicious Walkers in a Potential
We consider N vicious walkers moving in one dimension in a one-body potential
v(x). Using the backward Fokker-Planck equation we derive exact results for the
asymptotic form of the survival probability Q(x,t) of vicious walkers initially
located at (x_1,...,x_N) = x, when v(x) is an arbitrary attractive potential.
Explicit results are given for a square-well potential with absorbing or
reflecting boundary conditions at the walls, and for a harmonic potential with
an absorbing or reflecting boundary at the origin and the walkers starting on
the positive half line. By mapping the problem of N vicious walkers in zero
potential onto the harmonic potential problem, we rederive the results of
Fisher [J. Stat. Phys. 34, 667 (1984)] and Krattenthaler et al. [J. Phys. A
33}, 8835 (2000)] respectively for vicious walkers on an infinite line and on a
semi-infinite line with an absorbing wall at the origin. This mapping also
gives a new result for vicious walkers on a semi-infinite line with a
reflecting boundary at the origin: Q(x,t) \sim t^{-N(N-1)/2}.Comment: 5 page
Surface Magnetization of Aperiodic Ising Systems: a Comparative Study of the Bond and Site Problems
We investigate the influence of aperiodic perturbations on the critical
behaviour at a second order phase transition. The bond and site problems are
compared for layered systems and aperiodic sequences generated through
substitution. In the bond problem, the interactions between the layers are
distributed according to an aperiodic sequence whereas in the site problem, the
layers themselves follow the sequence. A relevance-irrelevance criterion
introduced by Luck for the bond problem is extended to discuss the site
problem. It involves a wandering exponent for pairs, which can be larger than
the one considered before in the bond problem. The surface magnetization of the
layered two-dimensional Ising model is obtained, in the extreme anisotropic
limit, for the period-doubling and Thue-Morse sequences.Comment: 19 pages, Plain TeX, IOP macros + epsf, 6 postscript figures, minor
correction
Scaling of the atmosphere of self-avoiding walks
The number of free sites next to the end of a self-avoiding walk is known as
the atmosphere. The average atmosphere can be related to the number of
configurations. Here we study the distribution of atmospheres as a function of
length and how the number of walks of fixed atmosphere scale. Certain bounds on
these numbers can be proved. We use Monte Carlo estimates to verify our
conjectures. Of particular interest are walks that have zero atmosphere, which
are known as trapped. We demonstrate that these walks scale in the same way as
the full set of self-avoiding walks, barring an overall constant factor
Anisotropic Scaling in Layered Aperiodic Ising Systems
The influence of a layered aperiodic modulation of the couplings on the
critical behaviour of the two-dimensional Ising model is studied in the case of
marginal perturbations. The aperiodicity is found to induce anisotropic
scaling. The anisotropy exponent z, given by the sum of the surface
magnetization scaling dimensions, depends continuously on the modulation
amplitude. Thus these systems are scale invariant but not conformally invariant
at the critical point.Comment: 7 pages, 2 eps-figures, Plain TeX and epsf, minor correction
Conformal invariance and linear defects in the two-dimensional Ising model
Using conformal invariance, we show that the non-universal exponent eta_0
associated with the decay of correlations along a defect line of modified bonds
in the square-lattice Ising model is related to the amplitude A_0=xi_n/n of the
correlation length \xi_n(K_c) at the bulk critical coupling K_c, on a strip
with width n, periodic boundary conditions and two equidistant defect lines
along the strip, through A_0=(\pi\eta_0)^{-1}.Comment: Old paper, for archiving. 5 pages, 4 figures, IOP macro, eps
Проблема внедрения инноваций в Республике Беларусь
Статья посвящена особенностям инновационного развития Беларуси. Рассматриваются основные принципы инновационной политики Беларуси и проблемы, сдерживающие инновационную активность белорусской экономики
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