arXiv subjects
Publications and source records attributed to Francois David.
The scaling properties of selfavoiding polymerized membranes are studied using renormalization group methods. The scaling exponent νis calculated for the first time at two loop order. νis found to agree with the Gaussian variational estimate for large space dimension d and to be close to the Flory estimate for d=3.
We study the phase transitions of N-components generalized helimagnets that obey the symmetry breaking pattern O(N) x O(N-1) -> O(N-1)_diag . In the neighborhood of two dimensions, a D=2+epsilon renormalization group study reveals a rich fixed point structure as well as a nematic-like phase with partial spin ordering. In the physical case O(3) x O(2) -> O(2)_diag , relevant to real magnets with noncollinear ordering, we show that this implies an XY-like transition between the ordered phase and the nematic-like phase. A non-Abelian mean-field calculation qualitatively valid above four dimensions is shown to lead to the same picture but then the principal chiral fixed point, which had been proposed earlier as the relevant fixed point for D=3 helimagnets, plays no role due to the appearance of a first-order line.
These lectures deal with: (1) a brief review of the theory of flexible random manifolds (with fixed intrinsic metric), connected to the physics of polymerized membranes, and of the effect of extrinsic curvature (crumpling transitions); (2) a discussion of the effect of self-avoidance and its renormalization group treatment in term of a non-local field theory (this last part is not much different from cond-mat/9509096).
Recent progresses in the understanding of the scaling behavior of self-avoiding flexible polymerized membranes (tethered manifolds) are reviewed. They rely on a new general renormalization group approach for a class of models with non-local singular interactions. This approach allows to prove the existence of a epsilon-expansion for the scaling exponents, and validates the one loop results obtained by direct renormalization methods. Applications of the method to polymerized membranes at the tricritical Theta-point are presented.
In a recent letter (hep-lat/9311019) A. Patrascioiu and E. Seiler argued that when taking into account "superinstantons configurations" the perturbative expansion and the beta-function of the two-dimensional non-linear sigma-model are modified at two loops order. I point out that: (1) perturbation theory in a superinstanton background is infra-red singular beyond three loops; (2) the new infra-red singular terms, which change the two loop terms, come from singular operators - describing superinstanton insertions - in the OPE; (3) taking into account these operators, the beta-function is not modified. Therefore the results of Patrascioiu and Seiler do not contradict perturbation theory.