683 research outputs found
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
Critical behaviour near multiple junctions and dirty surfaces in the two-dimensional Ising model
We consider m two-dimensional semi-infinite planes of Ising spins joined
together through surface spins and study the critical behaviour near to the
junction. The m=0 limit of the model - according to the replica trick -
corresponds to the semi-infinite Ising model in the presence of a random
surface field (RSFI). Using conformal mapping, second-order perturbation
expansion around the weakly- and strongly-coupled planes limits and
differential renormalization group, we show that the surface critical behaviour
of the RSFI model is described by Ising critical exponents with logarithmic
corrections to scaling, while at multiple junctions (m>2) the transition is
first order. There is a spontaneous junction magnetization at the bulk critical
point.Comment: Old paper, for archiving. 6 pages, 1 figure, IOP macro, 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
Scaling properties at the interface between different critical subsystems: The Ashkin-Teller model
We consider two critical semi-infinite subsystems with different critical
exponents and couple them through their surfaces. The critical behavior at the
interface, influenced by the critical fluctuations of the two subsystems, can
be quite rich. In order to examine the various possibilities, we study a system
composed of two coupled Ashkin-Teller models with different four-spin couplings
epsilon, on the two sides of the junction. By varying epsilon, some bulk and
surface critical exponents of the two subsystems are continuously modified,
which in turn changes the interface critical behavior. In particular we study
the marginal situation, for which magnetic critical exponents at the interface
vary continuously with the strength of the interaction parameter. The behavior
expected from scaling arguments is checked by DMRG calculations.Comment: 10 pages, 9 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
Surface Properties of Aperiodic Ising Quantum Chains
We consider Ising quantum chains with quenched aperiodic disorder of the
coupling constants given through general substitution rules. The critical
scaling behaviour of several bulk and surface quantities is obtained by exact
real space renormalization.Comment: 4 pages, RevTex, reference update
Marginal Extended Perturbations in Two Dimensions and Gap-Exponent Relations
The most general form of a marginal extended perturbation in a
two-dimensional system is deduced from scaling considerations. It includes as
particular cases extended perturbations decaying either from a surface, a line
or a point for which exact results have been previously obtained. The
first-order corrections to the local exponents, which are functions of the
amplitude of the defect, are deduced from a perturbation expansion of the
two-point correlation functions. Assuming covariance under conformal
transformation, the perturbed system is mapped onto a cylinder. Working in the
Hamiltonian limit, the first-order corrections to the lowest gaps are
calculated for the Ising model. The results confirm the validity of the
gap-exponent relations for the perturbed system.Comment: 11 pages, Plain TeX, eps
Critical behavior at the interface between two systems belonging to different universality classes
We consider the critical behavior at an interface which separates two
semi-infinite subsystems belonging to different universality classes, thus
having different set of critical exponents, but having a common transition
temperature. We solve this problem analytically in the frame of mean-field
theory, which is then generalized using phenomenological scaling
considerations. A large variety of interface critical behavior is obtained
which is checked numerically on the example of two-dimensional q-state Potts
models with q=2 to 4. Weak interface couplings are generally irrelevant,
resulting in the same critical behavior at the interface as for a free surface.
With strong interface couplings, the interface remains ordered at the bulk
transition temperature. More interesting is the intermediate situation, the
special interface transition, when the critical behavior at the interface
involves new critical exponents, which however can be expressed in terms of the
bulk and surface exponents of the two subsystems. We discuss also the smooth or
discontinuous nature of the order parameter profile.Comment: 16 pages, 9 figures, published version, minor changes, some
references adde
Fluctuating Bond Aggregation: a Model for Chemical Gel Formation
The Diffusion-Limited Cluster-Cluster Aggregation (DLCA) model is modified by
including cluster deformations using the {\it bond fluctuation} algorithm. From
3 computer simulations, it is shown that, below a given threshold value
of the volumic fraction , the realization of all intra-aggregate
bonding possibilities prevents the formation of a gelling network. For ,
the sol-gel transition occurs at a time which, in contrast to DLCA,
doesnot diverge with the box size. Several results are reported including small
angle scattering curves and possible applications are discussed.Comment: RevTex, 9 pages + 3 postscript figures appended using "uufiles". To
appear in Phys. Rev. Let
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