168 research outputs found
Surface-induced disorder and aperiodic perturbations at first-order transitions
In systems displaying a bulk first-order transition the order parameter may
vanish continuously at a free surface, a phenomenon which is called
surface-induced disorder. In the presence of surface-induced disorder the
correlation lengths, parallel and perpendicular to the surface, diverge at the
bulk transition point. In this way the surface induces an anisotropic power-law
singular behavior for some bulk quantities. For example in a finite system of
transverse linear size L, the response functions diverge as L^{(d-1)z+1}, where
d is the dimension of the system and z is the anisotropy exponent. We present a
general scaling picture for this anisotropic discontinuity fixed point. Our
phenomenological results are confronted with analytical and numerical
calculations on the 2D q-state Potts model in the large-q limit. The scaling
results are demonstrated to apply also for the same model with a layered,
Fibonacci-type modulation of the couplings for which the anisotropy exponent is
a continuous function of the strength of the quasiperiodic perturbation.Comment: 10 pages, 7 figures, epsf, RevTeX. Revised version, to appear in
Phys. Rev. B. More details given about the quantum Potts model. Minor
mistakes correcte
Comparative study of the critical behavior in one-dimensional random and aperiodic environments
We consider cooperative processes (quantum spin chains and random walks) in
one-dimensional fluctuating random and aperiodic environments characterized by
fluctuating exponents omega>0. At the critical point the random and aperiodic
systems scale essentially anisotropically in a similar fashion: length (L) and
time (t) scales are related as t ~ log^{1/omega}. Also some critical exponents,
characterizing the singularities of average quantities, are found to be
universal functions of omega, whereas some others do depend on details of the
distribution of the disorder. In the off-critical region there is an important
difference between the two types of environments: in aperiodic systems there
are no extra (Griffiths)-singularities.Comment: 13 pages RevTeX, 10 eps-figures include
Critical exponents of random XX and XY chains: Exact results via random walks
We study random XY and (dimerized) XX spin-1/2 quantum spin chains at their
quantum phase transition driven by the anisotropy and dimerization,
respectively. Using exact expressions for magnetization, correlation functions
and energy gap, obtained by the free fermion technique, the critical and
off-critical (Griffiths-McCoy) singularities are related to persistence
properties of random walks. In this way we determine exactly the decay
exponents for surface and bulk transverse and longitudinal correlations,
correlation length exponent and dynamical exponent.Comment: 4 pages RevTeX, 1 eps-figure include
Exact Renormalization-Group Study of Aperiodic Ising Quantum Chains and Directed Walks
We consider the Ising model and the directed walk on two-dimensional layered
lattices and show that the two problems are inherently related: The zero-field
thermodynamical properties of the Ising model are contained in the spectrum of
the transfer matrix of the directed walk. The critical properties of the two
models are connected to the scaling behavior of the eigenvalue spectrum of the
transfer matrix which is studied exactly through renormalization for different
self-similar distributions of the couplings. The models show very rich bulk and
surface critical behaviors with nonuniversal critical exponents,
coupling-dependent anisotropic scaling, first-order surface transition, and
stretched exponential critical correlations. It is shown that all the
nonuniversal critical exponents obtained for the aperiodic Ising models satisfy
scaling relations and can be expressed as functions of varying surface magnetic
exponents.Comment: 22 pages, 8 eps-figures, uses RevTex and epsf, minor correction
Random and aperiodic quantum spin chains: A comparative study
According to the Harris-Luck criterion the relevance of a fluctuating
interaction at the critical point is connected to the value of the fluctuation
exponent omega. Here we consider different types of relevant fluctuations in
the quantum Ising chain and investigate the universality class of the models.
At the critical point the random and aperiodic systems behave similarly, due to
the same type of extreme broad distribution of the energy scales at low
energies. The critical exponents of some averaged quantities are found to be a
universal function of omega, but some others do depend on other parameters of
the distribution of the couplings. In the off-critical region there is an
important difference between the two systems: there are no Griffiths
singularities in aperiodic models.Comment: 4 pages RevTeX, 2 eps-figures include
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