Nonperturbative fixed points and breakdown of Large-N analysis in O(N) models

藪中 俊介; Delamotte, B.*

Yabunaka, Shunsuke; Delamotte, B.*

We find that the multicritical fixed point structure of the O() models is much more complicated than widely believed. In particular, we find new nonperturbative fixed points in three dimensions () as well as at and for . These fixed points come together with an intricate homotopy structure when they are considered as functions of and . The fact that the new nonperturbative fixed points at had not been found questions the conventional large expansion, which plays a fundamental role in quantum and statistical field theory. We show on the example of the O model that at , its standard implementation misses in all dimensions below the new nonperturbative fixed points. These new fixed points show singularities under the form of cusps at in their effective potential that become a boundary layer at finite . We show that they have a physical impact on the multicritical physics of the ) model at finite . We also show that the boundary layer also plays a role for the tetracritical case , but in a different way than the tricritical case.