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論文

One fixed point can hide another one; Nonperturbative behavior of the tetracritical fixed point of O($$N$$) models at large $$N$$

藪中 俊介; Delamotte, B.*

Physical Review Letters, 130(26), p.261602_1 - 261602_6, 2023/06

We show that at $$N=infty$$ and below its upper critical dimension, $$d<d_{rm up}$$, the critical and tetracritical behaviors of the O$$(N)$$ models are associated with the same renormalization group fixed point (FP) potential. Only their derivatives make them different with the subtleties that taking their $$Ntoinfty$$ limit and deriving them do not commute and that two relevant eigenperturbations show singularities. This invalidates both the $$epsilon$$- and the $$1/N$$- expansions. We also show how the Bardeen-Moshe-Bander line of tetracritical FPs at $$N=infty$$ and $$d=d_{rm up}$$ can be understood from a finite-$$N$$ analysis.

論文

Incompleteness of the large-$$N$$ analysis of the $$O(N)$$ models; Nonperturbative cuspy fixed points and their nontrivial homotopy at finite $$N$$

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:0 パーセンタイル:53.2(Physics, Fluids & Plasmas)

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.

論文

Real-time observation of charge-spin cooperative dynamics driven by a nonequilibrium phonon environment

黒山 和幸*; 松尾 貞茂*; 村本 丈*; 藪中 俊介; Velentin, S. R.*; Ludwig, A.*; Wieck, A. D.*; 都倉 康弘*; 樽茶 清悟*

Physical Review Letters, 129(9), p.095901_1 - 095901_6, 2022/08

 被引用回数:1 パーセンタイル:48.58(Physics, Multidisciplinary)

We report on experimental observations of charge-spin cooperative dynamics of two-electron states in a GaAs double quantum dot located in a nonequilibrium phonon environment. When the phonon energy exceeds the lowest excitation energy in the quantum dot, the spin-flip rate of a single electron strongly enhances. In addition, originated from the spatial gradient of phonon density between the dots, the parallel spin states become more probable than the antiparallel ones. These results indicate that spin is essential for further demonstrations of single-electron thermodynamic systems driven by phonons, which will greatly contribute to understanding of the fundamental physics of thermoelectric devices.

論文

Isothermal transport of a near-critical binary fluid mixture through a capillary tube with the preferential adsorption

藪中 俊介; 藤谷 洋平*

Physics of Fluids, 34(5), p.052012_1 - 052012_18, 2022/05

 被引用回数:1 パーセンタイル:23(Mechanics)

弱い圧力、化学ポテンシャル勾配を加えた場合の毛細管中での二元混合系の等温環境下の輸送を考える。壁面での選択的吸着効果が強い際には、壁面近くに相関長程度の厚さの吸着層が形成される。そのため毛細管中の組成が不均一となり、相関長も不均一となる。我々はこのような状況での流体力学をLocal renormalized functional theoryを用いて考察し流量の計算を行った。

口頭

選択的吸着効果のもとでの二元混合系の毛管中質量流の臨界点近くのスケーリング則

藪中 俊介; 藤谷 洋平*

no journal, , 

弱い圧力,化学ポテンシャル勾配を加えた場合の毛細管中での二元混合系の浸透現象を考える。壁面での選択的吸着効果が強い際には、壁面近くに相関長程度の厚さの吸着層が形成される。そのため毛細管中の組成が不均一となり、相関長も不均一となる。我々はこのような状況での流体力学をLocal renormalized functional theoryを用いて考察し流量の計算を行ってきた。今回の講演では、流量の換算温度に関するスケーリング則に関して議論する。

口頭

Incompleteness of the large-N analysis of the O(N) models; Nonperturbative cuspy fixed points and their nontrivial homotopy at finite N

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.

口頭

A Fixed point can hide another one; The Nonperturbative behavior of the tetracritical fixed point of the O(N) models at large N

藪中 俊介; Delamotte, B.*

no journal, , 

We show that at $$N=infty$$ and below its upper critical dimension, $$d<d_{up}$$, the critical and tetracritical behaviors of the $$O(N)$$ models are associated with the same renormalization group fixed point (FP) potential. Only their derivatives make them different with the subtleties that taking their $$Ntoinfty$$ limit and deriving them do not commute and that two relevant eigenperturbations show singularities. This invalidates both the $$epsilon$$- and the $$1/N$$- expansions. We also show how the Bardeen-Moshe-Bander line of tetracritical FPs at $$N=infty$$ and $$d=d_{up}$$ can be understood from a finite-$$N$$ analysis.

口頭

Thermoosmosis of a near-critical binary fluid mixture under preferential adsorption; Universal flow properties

藪中 俊介; 藤谷 洋平*

no journal, , 

We consider a binary fluid mixture, which lies in the one-phase region near the demixing critical point, to consider its dynamics through a capillary tube. We assume preferential adsorption of one component on the tube's wall due to short-range interactions. The resultant adsorption layer becomes very thick near the critical point, inside which the thermal force density under a temperature gradient is nonvanishing. This enables a temperature difference to cause the total mass flow of the mixture, which represents thermoosmosis. We predict that, for any binary mixture near the critical point with the upper (lower) critical solution temperature, the direction of the total mass flow is the same as (opposite to) the temperature gradient, respectively.

口頭

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

藪中 俊介; Delamotte, B.*

no journal, , 

We find that the multicritical fixed point structure of the O($$N$$) models is much more complicated than widely believed. In particular, we find new nonperturbative fixed points in three dimensions ($$d=3$$) as well as at $$N = infty$$ and for $$3le d<4$$. These fixed points come together with an intricate homotopy structure when they are considered as functions of $$d$$ and $$N$$ $cite{ref}$. The fact that the new nonperturbative fixed points at $$N=infty$$ had not been found questions the conventional large $$N$$ expansion, which plays a fundamental role in quantum and statistical field theory. We show on the example of the O$$(N)$$ model that at $$N=infty$$, its standard implementation misses in all dimensions below $$d=4$$ the new nonperturbative fixed points. These new fixed points show singularities under the form of cusps at $$N=infty$$ in their effective potential that become a boundary layer at finite $$N$$. We show that they have a physical impact on the multicritical physics of the $$O(N$$) model at finite $$N$$. We also show that the boundary layer also plays a role for the tetracritical case $cite{tetra}$, but in a different way than the tricritical case.

口頭

The Nonperturbative behavior of the tricritical and tetracritical fixed points of the O(N) models at large N

藪中 俊介

no journal, , 

We study the Bardeen-Moshe-Bander lines in O (N) model at $$N=infty$$ in $$d=3$$ and 8/3. The first line in $$d=3$$ consists of the tricritical fixed points and ends at the Bardeen-Moshe-Bander fixed point. The large $$N$$ limit that allows us to find the BMB line must be taken on particular trajectories in the (d, N) plane: $$d= 3- alpha /N$$ and not at fixed dimension $$d= 3$$. Our study also reveals that the known BMB line is only half of the true line of fixed points, the second half being made of singular fixed points. The potentials of these singular fixed points show a cusp for a finite value of the field and their finite N counterparts a boundary layer. The second line in $$d=8/3$$ consists of the tricritical fixed points and ends at the Wison-Fisher fixed point. This seems paradoxical since the stabilities of the Wilson-Fisher fixed point and the tertactical fixed point are different. We show that only their derivatives of the potentials make them different with the subtleties that taking their limit and deriving them do not commute and that two relevant eigenperturbations show singularities at $$N=infty$$. We also discuss the finite-N realization of the second line of FPs in $$d=8/3$$.

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