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) models at large 藪中 俊介; Delamotte, B.*
Physical Review Letters, 130(26), p.261602_1 - 261602_6, 2023/06
被引用回数：0 パーセンタイル：0.00(Physics, Multidisciplinary)We show that at 
and below its upper critical dimension, 
, the critical and tetracritical behaviors of the O
models are associated with the same renormalization group fixed point (FP) potential. Only their derivatives make them different with the subtleties that taking their 
limit and deriving them do not commute and that two relevant eigenperturbations show singularities. This invalidates both the 
- and the 
- expansions. We also show how the Bardeen-Moshe-Bander line of tetracritical FPs at and 
can be understood from a finite- analysis.
analysis of the 
models; Nonperturbative cuspy fixed points and their nontrivial homotopy at finite 藪中 俊介; Fleming, C.*; Delamotte, B.*
Physical Review E, 106(5), p.054105_1 - 054105_29, 2022/11
被引用回数：4 パーセンタイル：60.75(Physics, Fluids & Plasmas)We summarize the usual implementations of the large- limit of models and show in detail why and how they can miss some physically important fixed points when they become singular in the infinite . Using Wilson's renormalization group in its functional nonperturbative versions, we show how the singularities build up as increases. In the Wilson-Polchinski version of the nonperturbative renormalization group, we show that the singularities are cusps, which become boundary layers for finite but large values of . The corresponding fixed points being never close to the Gaussian, are out of reach of the usual perturbative approaches. We find four new fixed points and study them in all dimensions and for all and show that they play an important role for the tricritical physics of models. Finally, we show that some of these fixed points are bi-valued when they are considered as functions of 
and thus revealing important and nontrivial homotopy structures.
藪中 俊介; Delamotte, B.*
no journal, ,
We show that at 
and below its upper critical dimension, 
, the critical and tetracritical behaviors of the models are associated with the same renormalization group fixed point (FP) potential. Only their derivatives make them different with the subtleties that taking their limit and deriving them do not commute and that two relevant eigenperturbations show singularities. This invalidates both the - and the - expansions. We also show how the Bardeen-Moshe-Bander line of tetracritical FPs at and 
can be understood from a finite- analysis.
藪中 俊介; Delamotte, B.*
no journal, ,
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.
藪中 俊介; Fleming, C.*; Delamotte, B.*
no journal, ,
We summarize the usual implementations of the large N limit of O(N) models and show in detail why and how they can miss some physically important fixed points when they become singular in the infinite N. Using Wilson's renormalization group in its functional nonperturbative versions, we show how the singularities build up as N increases. In the Wilson-Polchinski version of the nonperturbative renormalization group, we show that the singularities are cusps, which become boundary layers for finite but large values of N. The corresponding fixed points being never close to the Gaussian, are out of reach of the usual perturbative approaches. We find four new fixed points and study them in all dimensions and for all N and show that they play an important role for the tricritical physics of O(N) models. Finally, we show that some of these fixed points are bi-valued when they are considered as functions of d and N thus revealing important and nontrivial homotopy structures.
