2,632 research outputs found
Random Bond Potts Model: the Test of the Replica Symmetry Breaking
Averaged spin-spin correlation function squared
is calculated for the ferromagnetic
random bond Potts model. The technique being used is the renormalization group
plus conformal field theory. The results are of the - expansion type
fixed point calculation, being the deviation of the central charge
(or the number of components) of the Potts model from the Ising model value.
Calculations are done both for the replica symmetric and the replica symmetry
broken fixed points. The results obtained allow for the numerical simulation
tests to decide between the two different criticalities of the random bond
Potts model.Comment: 50 pages, Latex, 2 eps figure
The third parafermionic chiral algebra with the symmetry Z_{3}
We have constructed the parafermionic chiral algebra with the principal
parafermionic fields \Psi,\Psi^{+} having the conformal dimension
\Delta_{\Psi}=8/3 and realizing the symmetry Z_{3}.Comment: 6 pages, no figur
Spin--spin critical point correlation functions for the 2D random bond Ising and Potts models
We compute the combined two and three loop order correction to the spin-spin
correlation functions for the 2D Ising and q-states Potts model with random
bonds at the critical point. The procedure employed is the renormalisation
group approach for the perturbation series around the conformal field theories
representing the pure models. We obtain corrections for the correlations
functions which produce crossover in the amplitude but don't change the
critical exponent in the case of the Ising model and which produce a shift in
the critical exponent, due to randomness, in the case of the Potts model.
Comparison with numerical data is discussed briefly.Comment: 10pp, latex, PAR--LPTHE 94/1
Randomly coupled minimal models
Using 1-loop renormalisation group equations, we analyze the effect of
randomness on multi-critical unitary minimal conformal models. We study the
case of two randomly coupled models and found that they flow in two
decoupled models, in the infra-red limit. This result is then extend
to the case with randomly coupled models, which will flow toward
decoupled .Comment: 12 pages, latex, 1 eps figures; new results adde
Renormalization group flows for the second parafermionic field theory for N odd
Using the renormalization group approach, the Coulomb gas and the coset
techniques, the effect of slightly relevant perturbations is studied for the
second parafermionic field theory with the symmetry , for N odd. New
fixed points are found and classified
Operator algebra of the SL(2) conformal field theories
Structure constants of Operator Algebras for the SL(2) degenerate conformal
field theories are calculated.Comment: 10 pages, LaTeX2e, no figures, new refs and minor change
Coupled Minimal Models with and without Disorder
We analyse in this article the critical behavior of -state Potts
models coupled to -state Potts models () with and
without disorder. The technics we use are based on perturbed conformal
theories. Calculations have been performed at two loops. We already find some
interesting situations in the pure case for some peculiar values of and
with new tricritical points. When adding weak disorder, the results we obtain
tend to show that disorder makes the models decouple. Therefore, no relations
emerges, at a perturbation level, between for example the disordered -state Potts model and the two disordered -state Potts models
(), despite their central charges are similar according to recent
numerical investigations.Comment: 45 pages, Latex, 3 PS figure
Compatible associative products and trees
We compute dimensions of graded components for free algebras with two
compatible associative products, and give a combinatorial interpretation of
these algebras in terms of planar rooted trees.Comment: 19 pages, added a note on relation to other operad
Replica solution of the Random Energy Model
The alternative replica technique which involve summation over all integer
momenta of the partition function and which does not require analytic
continuation to non-integer values of the replica parameter is discussed.
In terms of this technique (which does not involve any replica symmetry
breaking "magic operations") rigorous solution for the average free energy of
the Random Energy Model is recovered in a very simple way.Comment: 8 page
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