Higher moments of spin-spin correlation functions for the ferromagnetic random bond Potts model

Using CFT techniques, we compute the disorder-averaged p-th power of the spin-spin correlation function for the ferromagnetic random bonds Potts model. We thus generalize the calculation of Dotsenko, Dotsenko and Picco, where the case p=2 was considered. Perturbative calculations are made up to the second order in epsilon (epsilon being proportional to the central charge deviation of the pure model from the Ising model value). The explicit dependence of the correlation function on $p$ gives an upper bound for the validity of the expansion, which seems to be valid, in the three-states case, only if p-alpha in final formula

Scale Invariance and Self-averaging in disordered systems

In a previous paper we found that in the random field Ising model at zero temperature in three dimensions the correlation length is not self-averaging near the critical point and that the violation of self-averaging is maximal. This is due to the formation of bound states in the underlying field theory. We present a similar study for the case of disordered Potts and Ising ferromagnets in two dimensions near the critical temperature. In the random Potts model the correlation length is not self-averaging near the critical temperature but the violation of self-averaging is weaker than in the random field case. In the random Ising model we find still weaker violations of self-averaging and we cannot rule out the possibility of the restoration of self-averaging in the infinite volume limit.Comment: 7 pages, 4 ps figure

Replica Symmetry Breaking and the Renormalization Group Theory of the Weakly Disordered Ferromagnet

We study the critical properties of the weakly disordered $p$-component ferromagnet in terms of the renormalization group (RG) theory generalized to take into account the replica symmetry breaking (RSB) effects coming from the multiple local minima solutions of the mean-field equations. It is shown that for $p < 4$ the traditional RG flows at dimensions $D=4-\epsilon$, which are usually considered as describing the disorder-induced universal critical behavior, are unstable with respect to the RSB potentials as found in spin glasses. It is demonstrated that for a general type of the Parisi RSB structures there exists no stable fixed points, and the RG flows lead to the {\it strong coupling regime} at the finite scale $R_{*} \sim \exp(1/u)$, where $u$ is the small parameter describing the disorder. The physical concequences of the obtained RG solutions are discussed. In particular, we argue, that discovered RSB strong coupling phenomena indicate on the onset of a new spin glass type critical behaviour in the temperature interval $\tau < \tau_{*} \sim \exp(-1/u)$ near $T_{c}$. Possible relevance of the considered RSB effects for the Griffith phase is also discussed.Comment: 32 pages, Late

Cooperative behavior of qutrits with dipole-dipole interactions

We have identified a class of many body problems with analytic solution beyond the mean-field approximation. This is the case where each body can be considered as an element of an assembly of interacting particles that are translationally frozen multi-level quantum systems and that do not change significantly their initial quantum states during the evolution. In contrast, the entangled collective state of the assembly experiences an appreciable change. We apply this approach to interacting three-level systems.Comment: 5 pages, 3 figures. Minor correction

Effect of Random Impurities on Fluctuation-Driven First Order Transitions

We analyse the effect of quenched uncorrelated randomness coupling to the local energy density of a model consisting of N coupled two-dimensional Ising models. For N>2 the pure model exhibits a fluctuation-driven first order transition, characterised by runaway renormalisation group behaviour. We show that the addition of weak randomness acts to stabilise these flows, in such a way that the trajectories ultimately flow back towards the pure decoupled Ising fixed point, with the usual critical exponents alpha=0, nu=1, apart from logarithmic corrections. We also show by examples that, in higher dimensions, such transitions may either become continuous or remain first order in the presence of randomness.Comment: 13 pp., LaTe

Non-perturbative phenomena in the three-dimensional random field Ising model

The systematic approach for the calculations of the non-perturbative contributions to the free energy in the ferromagnetic phase of the random field Ising model is developed. It is demonstrated that such contributions appear due to localized in space instanton-like excitations. It is shown that away from the critical region such instanton solutions are described by the set of the mean-field saddle-point equations for the replica vector order parameter, and these equations can be formally reduced to the only saddle-point equation of the pure system in dimensions (D-2). In the marginal case, D=3, the corresponding non-analytic contribution is computed explicitly. Nature of the phase transition in the three-dimensional random field Ising model is discussed.Comment: 12 page

Numerical Results For The 2D Random Bond 3-state Potts Model

We present results of a numerical simulation of the 3-state Potts model with random bond, in two dimension. In particular, we measure the critical exponent associated to the magnetization and the specific heat. We also compare these exponents with recent analytical computations.Comment: 9 pages, latex, 3 Postscript figure

The One-dimensional KPZ Equation and the Airy Process

Our previous work on the one-dimensional KPZ equation with sharp wedge initial data is extended to the case of the joint height statistics at n spatial points for some common fixed time. Assuming a particular factorization, we compute an n-point generating function and write it in terms of a Fredholm determinant. For long times the generating function converges to a limit, which is established to be equivalent to the standard expression of the n-point distribution of the Airy process.Comment: 15 page

Coulomb integrals for the SL(2,R) WZNW model

We review the Coulomb gas computation of three-point functions in the SL(2,R) WZNW model and obtain explicit expressions for generic states. These amplitudes have been computed in the past by this and other methods but the analytic continuation in the number of screening charges required by the Coulomb gas formalism had only been performed in particular cases. After showing that ghost contributions to the correlators can be generally expressed in terms of Schur polynomials we solve Aomoto integrals in the complex plane, a new set of multiple integrals of Dotsenko-Fateev type. We then make use of monodromy invariance to analytically continue the number of screening operators and prove that this procedure gives results in complete agreement with the amplitudes obtained from the bootstrap approach. We also compute a four-point function involving a spectral flow operator and we verify that it leads to the one unit spectral flow three-point function according to a prescription previously proposed in the literature. In addition, we present an alternative method to obtain spectral flow non-conserving n-point functions through well defined operators and we prove that it reproduces the exact correlators for n=3. Independence of the result on the insertion points of these operators suggests that it is possible to violate winding number conservation modifying the background charge.Comment: Improved presentation. New section on spectral flow violating correlators and computation of a four-point functio

Stability of critical behaviour of weakly disordered systems with respect to the replica symmetry breaking

A field-theoretic description of the critical behaviour of the weakly disordered systems is given. Directly, for three- and two-dimensional systems a renormalization analysis of the effective Hamiltonian of model with replica symmetry breaking (RSB) potentials is carried out in the two-loop approximation. For case with 1-step RSB the fixed points (FP's) corresponding to stability of the various types of critical behaviour are identified with the use of the Pade-Borel summation technique. Analysis of FP's has shown a stability of the critical behaviour of the weakly disordered systems with respect to RSB effects and realization of former scenario of disorder influence on critical behaviour.Comment: 10 pages, RevTeX. Version 3 adds the $\beta$ functions for arbitrary dimension of syste