arXiv subjects
Publications and source records attributed to P. Azaria.
We discuss examples of (1+1)-dimensional models where the perturbative renormalization group (RG) indicates a tendency to restore the symmetry in the strong coupling limit. We show that such restoration does occur sometimes, but the pertubative RG cannot be reliably used to detect it.
We study the classical ${SU(N)\otimes U(1)/SU(N-1)\otimes U(1)}$ Non Linear Sigma model which is the continuous low energy effective field theory for $N$ component frustrated spin systems. The $β$ functions for the two coupling constants of this model are calculated around two dimensions at two loop order in a low temperature expansion. Our study is completed by a large $N$ analysis of the model. The $β$ functions for the coupling constants and the mass gap are calculated in all dimensions between 2 and 4 at order ${1/N}$. As a main result we show that the standard procedure at the basis of the $1/N$ expansion leads to results that partially contradict those of the weak coupling analysis. We finally present the procedure that reconciles the weak coupling and large $N$ analysis, giving a consistent picture of the expected scaling of frustrated magnets.
We study a non linear sigma model $O(N)\otimes O(2)/O(N-2)\otimes O(2)$ describing the phase transition of N-components helimagnets up to two loop order in $D=2+ε$ dimensions. It is shown that a stable fixed point exists as soon as $N$ is greater than 3 (or equal). In the N=3 case, the symmetry of the system is dynamically enlarged at the fixed point to O(4) We show that the order parameter for Heisenberg helimagnets involves a tensor representation of $O(4)$. We show that for large $N$ and in the neighborhood of two dimensions this nonlinear sigma model describes the same critical theory as the Landau-Ginzburg linear theory. We deduce that there exists a dividing line $N_c (D)$ in the plane $(N, D)$ separating a first-order region containing the Heisenberg point at $D=4$ and a second-order region containing the whole $D=2$ axis. We conclude that the phase transition of Heisenberg helimagnets in dimension 3 is either first order or second order with $O(4)$ exponents involving a tensor representation or tricritical.