1,325 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

### Universal Ratios and Correlation Functions

We review some recent results concerning the quantitative analysis of the
universality classes of two-dimensional statistical models near their critical
point. We also discuss the exact calculation of the two--point correlation
functions of disorder operators in a free theory of complex bosonic and
fermionic field, correlators ruled by a Painleve differential equation.Comment: 10 pages, JHEP Proceedings of the Workshop on Integrable Theories,
Solitons and Duality, IFT-Unesp, Sao Paulo, Brasi

### 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, $\phi_{1,2}$ 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 $\phi_{1,3}$ and $\phi_{1,2}$ 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 $q$-state Potts model at and the O(n)
vector model are all described by the same perturbed conformal field theory.Comment: 22 pages, late

### The Field Theory of the q->4+ Potts Model

The q-state Potts model in two dimensions exhibits a first-order transition
for q>4. As q->4+ the correlation length at this transition diverges. We argue
that this limit defines a massive integrable quantum field theory whose lowest
excitations are kinks connecting 4+1 degenerate ground states. We construct the
S-matrix of this theory and the two-particle form factors, and hence estimate a
number of universal amplitude ratios. These are in very good agreement with the
results of extrapolated series in q^(-1/2) as well as Monte Carlo results for
q=5.Comment: 8 pages, 1 figure; late

### Field theory of scaling lattice models. The Potts antiferromagnet

In contrast to what happens for ferromagnets, the lattice structure
participates in a crucial way to determine existence and type of critical
behaviour in antiferromagnetic systems. It is an interesting question to
investigate how the memory of the lattice survives in the field theory
describing a scaling antiferromagnet. We discuss this issue for the square
lattice three-state Potts model, whose scaling limit as T->0 is argued to be
described exactly by the sine-Gordon field theory at a specific value of the
coupling. The solution of the scaling ferromagnetic case is recalled for
comparison. The field theory describing the crossover from antiferromagnetic to
ferromagnetic behaviour is also introduced.Comment: 11 pages, to appear in the proceedings of the NATO Advanced Research
Workshop on Statistical Field Theories, Como 18-23 June 200

### Susceptibility amplitude ratios in the two-dimensional Potts model and percolation

The high-temperature susceptibility of the $q$-state Potts model behaves as
$\Gamma|T-T_c|^{-\gamma}$ as $T\to T_c+$, while for $T\to T_c-$ one may define
both longitudinal and transverse susceptibilities, with the same power law but
different amplitudes $\Gamma_L$ and $\Gamma_T$. We extend a previous analytic
calculation of the universal ratio $\Gamma/\Gamma_L$ in two dimensions to the
low-temperature ratio $\Gamma_T/\Gamma_L$, and test both predictions with Monte
Carlo simulations for $q=3$ and 4. The data for $q=4$ are inconclusive owing to
large corrections to scaling, while for $q=3$ they appear consistent with the
prediction for $\Gamma_T/\Gamma_L$, but not with that for $\Gamma/\Gamma_L$. A
simple extrapolation of our analytic results to $q\to1$ indicates a similar
discrepancy with the corresponding measured quantities in percolation. We point
out that stronger assumptions were made in the derivation of the ratio
$\Gamma/\Gamma_L$, and our work suggests that these may be unjustified.Comment: 17 pages, late

### Correlation Functions in the Two-dimensional Ising Model in a Magnetic Field at $T=T_c$

The one and two-particle form factors of the energy operator in the
two-dimensional Ising model in a magnetic field at $T=T_c$ are exactly computed
within the form factor bootstrap approach. Together with the matrix elements of
the magnetisation operator already computed in ref.\,\cite{immf}, they are used
to write down the large distance expansion for the correlators of the two
relevant fields of the model.Comment: 18 pages, latex, 7 table

### 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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