60 research outputs found
Twist operator correlation functions in O(n) loop models
Using conformal field theoretic methods we calculate correlation functions of
geometric observables in the loop representation of the O(n) model at the
critical point. We focus on correlation functions containing twist operators,
combining these with anchored loops, boundaries with SLE processes and with
double SLE processes.
We focus further upon n=0, representing self-avoiding loops, which
corresponds to a logarithmic conformal field theory (LCFT) with c=0. In this
limit the twist operator plays the role of a zero weight indicator operator,
which we verify by comparison with known examples. Using the additional
conditions imposed by the twist operator null-states, we derive a new explicit
result for the probabilities that an SLE_{8/3} wind in various ways about two
points in the upper half plane, e.g. that the SLE passes to the left of both
points.
The collection of c=0 logarithmic CFT operators that we use deriving the
winding probabilities is novel, highlighting a potential incompatibility caused
by the presence of two distinct logarithmic partners to the stress tensor
within the theory. We provide evidence that both partners do appear in the
theory, one in the bulk and one on the boundary and that the incompatibility is
resolved by restrictive bulk-boundary fusion rules.Comment: 18 pages, 8 figure
Fluctuation force exerted by a planar self-avoiding polymer
Using results from Schramm Loewner evolution (SLE), we give the expression of
the fluctuation-induced force exerted by a polymer on a small impenetrable
disk, in various 2-dimensional domain geometries. We generalize to two polymers
and examine whether the fluctuation force can trap the object into a stable
equilibrium. We compute the force exerted on objects at the domain boundary,
and the force mediated by the polymer between such objects. The results can
straightforwardly be extended to any SLE interface, including Ising,
percolation, and loop-erased random walks. Some are relevant for extremal value
statistics.Comment: 7 pages, 22 figure
Spin interfaces in the Ashkin-Teller model and SLE
We investigate the scaling properties of the spin interfaces in the
Ashkin-Teller model. These interfaces are a very simple instance of lattice
curves coexisting with a fluctuating degree of freedom, which renders the
analytical determination of their exponents very difficult. One of our main
findings is the construction of boundary conditions which ensure that the
interface still satisfies the Markov property in this case. Then, using a novel
technique based on the transfer matrix, we compute numerically the left-passage
probability, and our results confirm that the spin interface is described by an
SLE in the scaling limit. Moreover, at a particular point of the critical line,
we describe a mapping of Ashkin-Teller model onto an integrable 19-vertex
model, which, in turn, relates to an integrable dilute Brauer model.Comment: 12 pages, 6 figure
General solution of an exact correlation function factorization in conformal field theory
We discuss a correlation function factorization, which relates a three-point
function to the square root of three two-point functions. This factorization is
known to hold for certain scaling operators at the two-dimensional percolation
point and in a few other cases. The correlation functions are evaluated in the
upper half-plane (or any conformally equivalent region) with operators at two
arbitrary points on the real axis, and a third arbitrary point on either the
real axis or in the interior. This type of result is of interest because it is
both exact and universal, relates higher-order correlation functions to
lower-order ones, and has a simple interpretation in terms of cluster or loop
probabilities in several statistical models. This motivated us to use the
techniques of conformal field theory to determine the general conditions for
its validity.
Here, we discover a correlation function which factorizes in this way for any
central charge c, generalizing previous results. In particular, the
factorization holds for either FK (Fortuin-Kasteleyn) or spin clusters in the
Q-state Potts models; it also applies to either the dense or dilute phases of
the O(n) loop models. Further, only one other non-trivial set of highest-weight
operators (in an irreducible Verma module) factorizes in this way. In this case
the operators have negative dimension (for c < 1) and do not seem to have a
physical realization.Comment: 7 pages, 1 figure, v2 minor revision
Critical domain walls in the Ashkin-Teller model
We study the fractal properties of interfaces in the 2d Ashkin-Teller model.
The fractal dimension of the symmetric interfaces is calculated along the
critical line of the model in the interval between the Ising and the
four-states Potts models. Using Schramm's formula for crossing probabilities we
show that such interfaces can not be related to the simple SLE, except
for the Ising point. The same calculation on non-symmetric interfaces is
performed at the four-states Potts model: the fractal dimension is compatible
with the result coming from Schramm's formula, and we expect a simple
SLE in this case.Comment: Final version published in JSTAT. 13 pages, 5 figures. Substantial
changes in the data production, analysis and in the conclusions. Added a
section about the crossing probability. Typeset with 'iopart
Critical interfaces of the Ashkin-Teller model at the parafermionic point
We present an extensive study of interfaces defined in the Z_4 spin lattice
representation of the Ashkin-Teller (AT) model. In particular, we numerically
compute the fractal dimensions of boundary and bulk interfaces at the
Fateev-Zamolodchikov point. This point is a special point on the self-dual
critical line of the AT model and it is described in the continuum limit by the
Z_4 parafermionic theory. Extending on previous analytical and numerical
studies [10,12], we point out the existence of three different values of
fractal dimensions which characterize different kind of interfaces. We argue
that this result may be related to the classification of primary operators of
the parafermionic algebra. The scenario emerging from the studies presented
here is expected to unveil general aspects of geometrical objects of critical
AT model, and thus of c=1 critical theories in general.Comment: 15 pages, 3 figure
Boundary conformal field theories and loop models
We propose a systematic method to extract conformal loop models for rational
conformal field theories (CFT). Method is based on defining an ADE model for
boundary primary operators by using the fusion matrices of these operators as
adjacency matrices. These loop models respect the conformal boundary
conditions. We discuss the loop models that can be extracted by this method for
minimal CFTs and then we will give dilute O(n) loop models on the square
lattice as examples for these loop models. We give also some proposals for WZW
SU(2) models.Comment: 23 Pages, major changes! title change
Time evolution of 1D gapless models from a domain-wall initial state: SLE continued?
We study the time evolution of quantum one-dimensional gapless systems
evolving from initial states with a domain-wall. We generalize the
path-integral imaginary time approach that together with boundary conformal
field theory allows to derive the time and space dependence of general
correlation functions. The latter are explicitly obtained for the Ising
universality class, and the typical behavior of one- and two-point functions is
derived for the general case. Possible connections with the stochastic Loewner
evolution are discussed and explicit results for one-point time dependent
averages are obtained for generic \kappa for boundary conditions corresponding
to SLE. We use this set of results to predict the time evolution of the
entanglement entropy and obtain the universal constant shift due to the
presence of a domain wall in the initial state.Comment: 27 pages, 10 figure
Hare: a file system for non-cache-coherent multicores
Hare is a new file system that provides a POSIX-like interface on multicore processors without cache coherence. Hare allows applications on different cores to share files, directories, and file descriptors. The challenge in designing Hare is to support the shared abstractions faithfully enough to run applications that run on traditional shared-memory operating systems, with few modifications, and to do so while scaling with an increasing number of cores.
To achieve this goal, Hare must support features (such as shared file descriptors) that traditional network file systems don't support, as well as implement them in a way that scales (e.g., shard a directory across servers to allow concurrent operations in that directory). Hare achieves this goal through a combination of new protocols (including a 3-phase commit protocol to implement directory operations correctly and scalably) and leveraging properties of non-cache-coherent multiprocessors (e.g., atomic low-latency message delivery and shared DRAM).
An evaluation on a 40-core machine demonstrates that Hare can run many challenging Linux applications (including a mail server and a Linux kernel build) with minimal or no modifications. The results also show these applications achieve good scalability on Hare, and that Hare's techniques are important to achieving scalability.Quanta Computer (Firm
Integral equations and large-time asymptotics for finite-temperature Ising chain correlation functions
This work concerns the dynamical two-point spin correlation functions of the
transverse Ising quantum chain at finite (non-zero) temperature, in the
universal region near the quantum critical point. They are correlation
functions of twist fields in the massive Majorana fermion quantum field theory.
At finite temperature, these are known to satisfy a set of integrable partial
differential equations, including the sinh-Gordon equation. We apply the
classical inverse scattering method to study them, finding that the ``initial
scattering data'' corresponding to the correlation functions are simply related
to the one-particle finite-temperature form factors calculated recently by one
of the authors. The set of linear integral equations (Gelfand-Levitan-Marchenko
equations) associated to the inverse scattering problem then gives, in
principle, the two-point functions at all space and time separations, and all
temperatures. From them, we evaluate the large-time asymptotic expansion ``near
the light cone'', in the region where the difference between the space and time
separations is of the order of the correlation length
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