9,222 research outputs found
Off-critical correlations in the Ashkin-Teller model
We use the exact scattering description of the scaling Ashkin-Teller model in
two dimensions to compute the two-particle form factors of the relevant
operators. These provide an approximation for the correlation functions whose
accuracy is tested against exact sum rules.Comment: 8 pages, late
Correlators in integrable quantum field theory. The scaling RSOS models
The study of the scaling limit of two-dimensional models of statistical
mechanics within the framework of integrable field theory is illustrated
through the example of the RSOS models. Starting from the exact description of
regime III in terms of colliding particles, we compute the correlation
functions of the thermal, and (for some cases) spin operators in
the two-particle approximation. The accuracy obtained for the moments of these
correlators is analysed by computing the central charge and the scaling
dimensions and comparing with the exact results. We further consider the
(generally non-integrable) perturbation of the critical points with both the
operators and and locate the branches solved on the
lattice within the associated two-dimensional phase diagram. Finally we discuss
the fact that the RSOS models, the dilute -state Potts model at and the O(n)
vector model are all described by the same perturbed conformal field theory.Comment: 22 pages, late
On the space of quantum fields in massive two-dimensional theories
For a large class of integrable quantum field theories we show that the
S-matrix determines a space of fields which decomposes into subspaces labeled,
besides the charge and spin indices, by an integer k. For scalar fields k is
non-negative and is naturally identified as an off-critical extension of the
conformal level. To each particle we associate an operator acting in the space
of fields whose eigenvectors are primary (k=0) fields of the massive theory. We
discuss how the existing results for models as different as Z_n, sine-Gordon or
Ising with magnetic field fit into this classification.Comment: 17 page
Potts q-color field theory and scaling random cluster model
We study structural properties of the q-color Potts field theory which, for
real values of q, describes the scaling limit of the random cluster model. We
show that the number of independent n-point Potts spin correlators coincides
with that of independent n-point cluster connectivities and is given by
generalized Bell numbers. Only a subset of these spin correlators enters the
determination of the Potts magnetic properties for q integer. The structure of
the operator product expansion of the spin fields for generic q is also
identified. For the two-dimensional case, we analyze the duality relation
between spin and kink field correlators, both for the bulk and boundary cases,
obtaining in particular a sum rule for the kink-kink elastic scattering
amplitudes.Comment: 27 pages; 6 figures. Published version, some comments and references
adde
Decay of particles above threshold in the Ising field theory with magnetic field
The two-dimensional scaling Ising model in a magnetic field at critical
temperature is integrable and possesses eight stable particles A_i (i=1,...,8)
with different masses. The heaviest five lie above threshold and owe their
stability to integrability. We use form factor perturbation theory to compute
the decay widths of the first two particles above threshold when integrability
is broken by a small deviation from the critical temperature. The lifetime
ratio t_4/t_5 is found to be 0.233; the particle A_5 decays at 47% in the
channel A_1A_1 and for the remaining fraction in the channel A_1A_2. The
increase of the lifetime with the mass, a feature which can be expected in two
dimensions from phase space considerations, is in this model further enhanced
by the dynamics.Comment: 15 pages, 5 figures; minor typos correcte
Universal ratios along a line of critical points. The Ashkin--Teller model
The two-dimensional Ashkin-Teller model provides the simplest example of a
statistical system exhibiting a line of critical points along which the
critical exponents vary continously. The scaling limit of both the paramagnetic
and ferromagnetic phases separated by the critical line are described by the
sine-Gordon quantum field theory in a given range of its dimensionless
coupling. After computing the relevant matrix elements of the order and
disorder operators in this integrable field theory, we determine the universal
amplitude ratios along the critical line within the two-particle approximation
in the form factor approach.Comment: 31 pages, late
Field theory of Ising percolating clusters
The clusters of up spins of a two-dimensional Ising ferromagnet undergo a
second order percolative transition at temperatures above the Curie point. We
show that in the scaling limit the percolation threshold is described by an
integrable field theory and identify the non-perturbative mechanism which
allows the percolative transition in absence of thermodynamic singularities.
The analysis is extended to the Kertesz line along which the Coniglio-Klein
droplets percolate in a positive magnetic field.Comment: 19 pages, 8 figure
First order phase transitions and integrable field theory. The dilute q-state Potts model
We consider the two-dimensional dilute q-state Potts model on its first order
phase transition surface for 0<q\leq 4. After determining the exact scattering
theory which describes the scaling limit, we compute the two-kink form factors
of the dilution, thermal and spin operators. They provide an approximation for
the correlation functions whose accuracy is illustrated by evaluating the
central charge and the scaling dimensions along the tricritical line.Comment: 21 pages, late
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