カイラル磁気効果は量子色力学の動的ユニバーサリティクラスに影響を与えるのか?
曽我部 紀之（慶応大学）

共同研究者: 本郷 優 (RIKEN iTHEMS)、山本 直希（慶応大学）

非平衡系の物理学−階層性と普遍性−
2018年12月26日 京都大学 基礎物理学研究所
Masaru Hongo, NS, Naoki Yamamoto, JHEP 1811, 108 (2018)

普遍的な物理現象
例1. 相転移・臨界現象
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磁性体
超流動体
クォーク・グルーオン・プラズマ

例2. トポロジカル輸送現象-

量子ホール効果
カイラル輸送現象

重イオン衝突実験• QCD（量子色力学）相転移・臨界現象 • カイラル輸送現象
ユニバーサリティクラス- （臨界点の実験的兆候）--

カイラル磁気効果
カイラル分離効果（カイラル渦効果）

https://www.bnl.gov/physics/best/

カイラル磁気効果はQCDのユニバーサリティクラスに影響を与えるのか？

動的ユニバーサリティクラス

P. C. Hohenberg and B. I. Halperin (1977)

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動的ユニバーサリティクラス

P. C. Hohenberg and B. I. Halperin (1977)

微視的な理論

低エネルギー有効理論
流体力学変数：
粗視化

⇠

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秩序変数

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保存電荷

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南部・Goldstoneモード⇤ 1<latexit sha1_base64="Wtx1+SyKPNxNwvvzOiFWU+m/9XI=">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</latexit>
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同じ対称性
対称性とギャップレスモードに基づく臨界現象の分類

動的ユニバーサリティクラス

P. C. Hohenberg and B. I. Halperin (1977)

カイラリティ
スピン

運動量

右巻き電荷：QR

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電荷
軸性電荷

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sha1_base64="4qF11DJqlElZ4WiC8xDvDB+CHfM=">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</latexit>

Q ⌘ QR + QL

QA ⌘ QR

QL

磁場中のカイラル輸送現象

Vilenkin (1980), Nielsen and Ninomiya(1983)
Kharzeev, McLerran, and Warringa (2008)
Fukushima, Kharzeev, and Warringa (2008)

B

スピン

運動量

e2 µR
jR =
B
2
4⇡
jL =

カイラル磁気効果：<latexit sha1_base64="(null)">(null)</latexit>

カイラル分離効果：<latexit sha1_base64="(null)">(null)</latexit>

e2 µA
j=
B
2
2⇡

e2 µ
jA = 2 B
2⇡トポロジーと関係した係数<latexit sha1_base64="(null)">(null)</latexit>

µA ⌘

e2 µL
B
2
4⇡

µR

µL
2

µR + µLµ⌘
2c.f. 量子ホール効果

カイラル磁気波

G. M. Newman (2006)
D. E. Kharzeev and H. Yee (2011)

B

分離効果

@2 n
e4 B 2
2
=
r
n
2
4
@t
4⇡
A

2

jA =

磁気効果
e2 µA
j=
B
2
2⇡

<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>

e µ
B
2
2⇡
<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>| n| > 0| nA | > 0<latexit sha1_base64="(null)">(null)</latexit>

···

n
⌘
µ

感受率:

| nA | > 0

カイラル輸送現象に特有なギャップレスモード
動的ユニバーサリティクラスへの影響？

<latexit sha1_base64="uhThJPd3mIqeiNWGJ+vWlZkL+j8=">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</latexit>
sha1_base64="SPOOkB9a9PLPI62tDh40fQpr0P0=">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</latexit>

nA
A ⌘
µA
<latexit sha1_base64="(null)">(null)</latexit>

結果
カイラル磁気効果は
動的ユニバーサリティクラスを変える

磁場中のカイラル2次相転移の動的ユニバーサリティクラス
C: カイラル磁気係数 ( j = CµA B )<latexit sha1_base64="(null)">(null)</latexit>

C=0

C≠0

モデル E (xyモデル)

モデル A (イジングモデル)
M. Hongo, NS, N. Yamamoto (2018)

もくじ
1

セットアップ2

定式化-

Ginzburg-Landau自由エネルギー-

Langevin方程式3

くりこみ群解析4

まとめセットアップ• QCD at 有限 T, µ , BI<latexit sha1_base64="(null)">(null)</latexit>

2成分の無質量クォーク• カイラル対称性<latexit sha1_base64="xMI1WEWvPtVSvDh31W/E7lUapsY=">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</latexit>
sha1_base64="J09EKrUCEWR/KHADJEX/LF8nKPo=">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</latexit>

q=

✓

u
d

◆

アイソスピン空間<latexit sha1_base64="TP/9OiK21h5LO7IPsXeQhU+hWcE=">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</latexit>
sha1_base64="8b5+yVyWGNuHk6u+Mk23aYcMv+M=">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</latexit>

アイソスピン化学ポテンシャル:µI ⌘ µu µd<latexit sha1_base64="f9Z3Z13PBBdizQYIuPeZqb2X66k=">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</latexit>
sha1_base64="ZNE7lWcznoLX1KW5+dhQaKzJVt4=">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</latexit>

B=0<latexit sha1_base64="hkfrO+JkAm+LAVlqDhJqlOd02R4=">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</latexit>
sha1_base64="BG2IeDQQ8uvT72kidQ+WLvUCPL8=">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</latexit>

SU(2)L ⇥ SU(2)R<latexit sha1_base64="(null)">(null)</latexit>

qL,R ! e

a
i✓L,R
⌧a

<latexit sha1_base64="(null)">(null)</latexit>

qL,R<latexit sha1_base64="(null)">(null)</latexit>

B 6= 0U(1)3L ⇥ U(1)3R

qL,R ! e

3
i✓L,R
⌧3

SU(2) の生成子：⌧ a (a = 1, 2, 3)• カイラル対称性の破れの2次相転移<latexit sha1_base64="Y6dbdGAV3wL4ELCKCosbj7N7R8w=">AAAFj3ichZTNbtNAEICnAUMJP23ggsQlIipqL9W6QgrigKJyKbe2wW2lpKpsd9uuYq+3thOaWnkB7ogDEggkDojH4MILcOgjII5F4sKB2bHpj6PYa3k9O55vZnZndx3liShm7GSqcuWqce369I3qzVu378zM1u5uREE/dLnlBl4Qbjl2xD0huRWL2ONbKuS273h80+k91/83BzyMRCBfxkPFt317X4o94doxqjpJN/TrbWs0v7SwM9tgi4xafVwwM6EBWVsNapUmdGEXAnChDz5wkBCj7IENET4dMIGBQt02JKgLURL0n8MIqsj20YqjhY3aHvb7OOpkWolj7TMi2sUoHr4hknWYYz/YF3bKvrOv7Cf7O9FXQj50LkP8OinL1c7M6/vtP6WUj98YDs6pwpxj2IMnlKvA3BVp9CzclB8cvz1tP12fSx6xT+wX5v+RnbBvOAM5+O1+XuPr7wrycTCXySuWYGSOM5RopTI7iZpXtGo+zUNinRKqlkAPowuyonoNUYqxP6/NJA8hDIjXss6rTjUpZo4yJiUSHJcRh7kYh6XELj5pDL3uR9gnpCmmrDHGKmV6udn0SgmVI1QpsZwjlkuJY9RfZtgZE9JOHOe6Z/n9P5027oDiOPpcXoySahzaRWXxtLVH1px2mqR7Q5C/eeKCzDbJPPi4J0ewQH6reEOZ+ftoXNhYWjRRXnvcaK1kd9U0PICHGMGEJrRgBVaxyjqzN/AePhg1o2k8M1qpaWUqY+7BpWa8+AdLYy6k</latexit>
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c.f. 回転対称性の破れ（強磁性体）<latexit sha1_base64="6RNgPvZOXzLAcLRlpCUEEw/TM1Q=">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</latexit>
sha1_base64="gI5PTEk6VH3R+PZ0LAafbGEdhGk=">AAAFl3ichZTNbtNAEMenKYYSPpqUC4hLRChqpapaF6QiJERUJNRj05K2UlMi290WK/6q7YSmVl6AF+CAOIAECPEYXHgBDn0ExLFIXDjw99j0w1HitbyeHc9vZnZnd3XPMoNQiKOxwvgF5eKlicvFK1evXZ8slafWA7fjG7JhuJbrb+paIC3TkY3QDC256flSs3VLbujtp/H/ja70A9N1noc9T27b2p5j7pqGFkLVKpWbodZ5oTUrM9pjdW5h7v5sq1QV84JbZVBQU6Fau0vcVtxyYZGatEMuGdQhmyQ5FEK2SKMAzxapJMiDbpsi6HxIJv+X1Kci2A6sJCw0aNvo9zDaSrUOxrHPgGkDUSy8PsgKTYsf4os4Ft/FV/FT/B3qK2IfcS49fPWElV5r8vXNtT+5lI1vSC9PqZE5h7RLDzlXE7l7rIlnYSR89/DN8dqj1enonvggfiH/9+JIfMMMnO5v42Ndrr4dkY+OXIavWITIEjN0YOWldg40r3jVbJ6HgzpFXC0THvpnZI/r1YMUoj+tzTAPPnWZj+U4rwrXZDRzkDIJEWGcR+xnYuznEjt4khjxuh+gj1gzmmoMMI1cpp2ZTTuX8DKEl0ssZYilXOIQ+vOMOGF83omDXPMkv/+nU8MOGB0nPpdnoyQanXdRXrzY2mJryTvN4XvDZH8zzLmpbZR6sLEn+zTLfou4odTsfTQorC/Mq5DrD6q15eSqogm6TXcQQaVFqtEyraDKBrJ7R5/os3JLeaI8U1LbwljK3KBzTan/A5rbMLU=</latexit>

qL,R流体力学変数• 秩序変数↵ ⌘<latexit sha1_base64="OAQIZ6U8ddUvnMCbyh+dBKc0IfY=">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</latexit>
sha1_base64="785yor8/5IW4/QeCHa4C/X6EyyU=">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</latexit>✓

カイラル凝縮：• 保存電荷密度<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="O8nj9+qsDR5pKiTTlz4MHMBtYwA=">AAAFmnichZTNbtNAEICnAUMJP02BAxIcLKIiuERrVKkVpypcirj0L22luopsd5uuYq9/Y5paeQFegAMXQOJQeAwuvACHPgLiWCQuHBiPTX8cxV7L69nxfDOzO7trerYII8ZOpmpXrirXrk/fqN+8dfvOTGP27mboDgKLdyzXdoNt0wi5LSTvRCKy+bYXcMMxbb5l9l+m/7diHoTClRvR0OO7jtGTYl9YRoSqbuO+HoqeY+jcH4hYN41A9VW/22iyFqOmjgtaLjQhbyvubG0BdNgDFywYgAMcJEQo22BAiM8OaMDAQ90uJKgLUBL0n8MI6sgO0IqjhYHaPvY9HO3kWonj1GdItIVRbHwDJFWYYz/YMTtl39lX9pP9negrIR9pLkP8mhnLve7M2wfrfyopB78RHJxTpTlHsA+LlKvA3D3SpLOwMj4+ene6/mJtLnnCPrFfmP9HdsK+4Qxk/Nv6vMrX3pfkY2Iuk1cswcgcZyjRysvtJGre0Ko5NA+JdUqoWgI9jC7IHtVriFKE/XltJnkIICY+ldO8VKpJOXOYMxmR4LiK8Asx/EpiD58sRrruh9gnpCmnOmNMp5LpF2bTryS8AuFVEu0C0a4kjlB/mWFnTEA7cZzTz/L7fzoN3AHlcdJzeTFKpjFpF1XFS61tsua00yTdG4L8PSXOzW2T3IODe3IEz8hvHW8orXgfjQubz1saa2mr882l5fyumoaH8BgjaLAAS7AMK1hlC1fsAxzDF+WR0lZeKa8z09pUztyDS03Z+AcroTNX</latexit>
sha1_base64="BlJWgZJV9GWbcr0pUDPA5H04X3c=">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</latexit>⇡◆<latexit sha1_base64="(null)">(null)</latexit>

U(1)3L ⇥ U(1)3R を破る
中性パイオン： ⇡ ⌘ q̄i 5 ⌧ q
3

⌘ q̄q

<latexit sha1_base64="NMhBhoKnBuCNxDWApIYgvscj6UI=">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</latexit>
sha1_base64="BqGQ9iuqdDVtVku2c9Y096/93M8=">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</latexit>n ⌘ nL + nR

nA ⌘ n L

U(1)3L ⇥ U(1)3R のNoetherの定理<latexit sha1_base64="(null)">(null)</latexit>nR<latexit sha1_base64="(null)">(null)</latexit>(nL,R ⌘ q̄L,R 0 ⌧ 3 qL,R )Ginzburg-Landau自由エネルギーF =<latexit sha1_base64="(null)">(null)</latexit>

Z



r
1
2
dr ( ↵ ) + (r ↵ )2 + u( ↵ )2 (
2
2

1 2
1 2
) +
n +
nA + n 2↵22 A2

秩序変数での展開• 相転移点近傍
微分展開• 長距離間の振る舞いに興味
展開項に制限
• 対称性
カイラル対称性、時間反転・パリティ・荷電共役対称性

Langevin方程式@ ↵ (r, t)=@tF↵ (r, t)<latexit sha1_base64="(null)">(null)</latexit>ZF
dr [ ↵ (r, t), nA (r , t)]+ ⇠↵ (r, t)
0nA (r , t)00Poisson括弧

輸送係数[nA (r, t),

0 0↵ (r , t )] = g"↵(r, t) (rr 0 ) (t<latexit sha1_base64="(null)">(null)</latexit>

結合パラメタh⇠↵ (r, t)⇠ (r 0 , t0 )i = 2

↵

d

(r

揺動散逸関係式r 0 ) (t

t0 )

t0 )

Langevin方程式@n(r, t)F2
= r@tn(r, t)<latexit sha1_base64="(null)">(null)</latexit>ZF
dr [n(r, t), nA (r , t)]+ ⇣(r, t)
0nA (r , t)00Poisson括弧

輸送係数<latexit sha1_base64="(null)">(null)</latexit>[n(r, t), nA (r 0 , t)] = CB · r (rr 0 ) (tt0 )カイラル磁気係数

量子異常交換関係

R. Jackiw and K. Johnson (1969)
S. L. Adler and D. G. Boulware (1969)くりこみ群解析
1. Langevin方程式と等価な場の理論を構築

P. C. Martin, E. D. Siggia, and A. Rose (1973), H-K. Janssen (1976), C. De Dominicis (1978)

2. 場の理論の計算手法を使う- ファインマンルール- 摂動展開 (✏ = 4 d 展開・1ループ）- くりこみ群方程式

動的臨界指数<latexit sha1_base64="oEdlhQXdLL1K8JDWJ5UYtDt0Rvw=">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</latexit>
sha1_base64="oYwhbn1RhNtgzNJ99MIxwVhYsOE=">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</latexit>! 0 = bz !

<latexit sha1_base64="ozJmTaH3ZwFcJYavGM8omyfZfVk=">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</latexit>
sha1_base64="IOJuRLMmnhu6QWxaZImD8skyhPs=">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</latexit>

変数： wA ⌘g2 ⇤ ✏
, f⌘
, w⌘
2
8⇡ A
A A

くりこみスケール
C|B|, h⌘ pA⇤<latexit sha1_base64="(null)">(null)</latexit>

カットオフ運動量

くりこみ群フローg2 ⇤ ✏
, f⌘
, w⌘
2
8⇡ A
A A

変数： wA ⌘C|B|, h⌘ pA⇤<latexit sha1_base64="(null)">(null)</latexit>

Flow diagram for (i) and (ii)(w,
カイラル磁気効果なし(vl h), wl=, hl(0,) =0)(v1, w1 , h1 ) = (✏/20, 0, 0)<latexit sha1_base64="/L7eI1eY+byqeCViBcwi3DYHpMU=">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</latexit>

1.5
(i)

ww
A5

1.0

モデルE
d
z=
2

0.5
<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="N0Zpz4fDSC2Twg5XGt2UXKfIFio=">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</latexit>
sha1_base64="OFVshI1l5/jxnIN+Oo85aM2dmFE=">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</latexit>

0.0

(ii)

<latexit sha1_base64="(null)">(null)</latexit>

-0.5
0.0

0.5

1.0

f

1.5

くりこみ群フロー
変数： wA ⌘g2 ⇤ ✏
, f⌘
, w⌘
2
8⇡ A
A A

C|B|
, h⌘ pA⇤<latexit sha1_base64="(null)">(null)</latexit>(w, h) = (104 , 100 )(104 , 106 )<latexit sha1_base64="U3lTNlfEYmolR0X2v8UJdFQztKg=">AAAFl3ichZTNbtNAEMenKYYSPpqUC4hLRFSUSFW1RpWKkBBVkVCPTUvaSm2JbHfbWvFXbSdtauUFeAEOiANIgBCPwYUX4NBHQByLxIUDf49NPxLFXsvr2fH8ZmZ3dlf3LDMIhTgZK4xfUa5em7hevHHz1u3JUnlqLXA7viGbhmu5/oauBdIyHdkMzdCSG54vNVu35Lrefh7/X+9KPzBd52XY8+S2re055q5paCFUrVK5djizX39aU8WruRl0ot4qVcWs4FYZFtRUqFLalt1yYZ62aIdcMqhDNklyKIRskUYBnk1SSZAH3TZF0PmQTP4vqU9FsB1YSVho0LbR72G0mWodjGOfAdMGolh4fZAVmhY/xBdxKr6Lr+Kn+DvSV8Q+4lx6+OoJK73W5Ou7q39yKRvfkPbPqcycQ9qlx5yridw91sSzMBK+e/zmdPXJynT0UHwQv5D/e3EivmEGTve38bEhV95m5KMjl9ErFiGyxAwdWHmpnQPNIa+azfNwUKeIq2XCQ/+C7HG9epBC9Oe1GeXBpy7zsRznVeGaZDNHKZMQEcZ5xMFAjINcYgdPEiNe9yP0EWuyqeYQ08xl2gOzaecS3gDh5RKLA8RiLnEM/WVGnDE+78Rhbussv/+nU8MOyI4Tn8uLURKNzrsoL15sbbG15J3m8L1hsr8ac25qG6UebOzJPtXZbxE3lDp4Hw0La49mVciNuerCUnpXTdB9eoAIKs3TAi3RMqpsILt39Ik+K/eUZ8oLJbUtjKXMHbrUlMY/pg0viw==</latexit>
sha1_base64="tvOkMCm16Z01GJxTLS56wCBDGkY=">AAAFl3ichZTNbtNAEMenKaYlfDQpFxCXiFCUSFW1RpWKkBBRkVCPTUvaSm2JbHfbWvFXbSdtauUFeAEOiANIgBCPwYUX4NBHQByLxIUDf49NPxIlXsvr2fH8ZmZ3dlf3LDMIhTgZy41fUa5OTF7LX79x89ZUoTi9Frht35ANw7Vcf0PXAmmZjmyEZmjJDc+Xmq1bcl1vPY//r3ekH5iu8zLsenLb1vYcc9c0tBCqZqFYOZzdrz6tqOLV/Cw6UW0WymJOcCsNCmoqlGsPiNuyW8wt0BbtkEsGtckmSQ6FkC3SKMCzSSoJ8qDbpgg6H5LJ/yX1KA+2DSsJCw3aFvo9jDZTrYNx7DNg2kAUC68PskQz4of4Ik7Fd/FV/BR/h/qK2EecSxdfPWGl15x6fWf1TyZl4xvS/jk1MueQdukx52oid4818SyMhO8cvzldfbIyEz0UH8Qv5P9enIhvmIHT+W18rMuVtyPy0ZHL8BWLEFlihg6svNTOgeaQV83meTioU8TVMuGhd0H2uF5dSCH689oM8+BTh/lYjvMqcU1GM0cpkxARxlnEQV+Mg0xiB08SI173I/QRa0ZTjQGmkcm0+mbTyiS8PsLLJBb7iMVM4hj6y4w4Y3zeiYPc1ll+/0+nhh0wOk58Li9GSTQ676KseLG1xdaSd5rD94bJ/irMualtlHqwsSd7VGW/edxQav99NCisPZpTIdfny7Wl5KqiSbpH9xFBpQWq0RIto8oGsntHn+izcld5prxQUtvcWMrcpktNqf8Dl0sv7w==</latexit><latexit sha1_base64="oF9lo4rvRasTvxyJ2okJOr6XhLQ=">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</latexit>
sha1_base64="HBtygmd2P4rBj/toevatuoIHagQ=">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</latexit>

(i)

0.8

0.8

0.6

0.6

0.4

(iii)
<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>

(iii)

0.2

モデルE

0.0

(ii)

0.0

0.5

d
z=
2

(iv)

1.0

(i)

1.0

wwA5

wwA5

1.0

1.5

2.0

2.5

<latexit sha1_base64="(null)">(null)</latexit>

0.4

モデルA

0.2
0.0
0.0

0.5

f

拡散
<latexit sha1_base64="(null)">(null)</latexit>

(iv)

(ii)

1.0

1.5

2.0

<latexit sha1_base64="(null)">(null)</latexit>

2.5

f

h2
C2
⇠
w
A

カイラル磁気波<latexit sha1_base64="(null)">(null)</latexit>

拡散 ⌧ カイラル磁気波<latexit sha1_base64="(null)">(null)</latexit>

z=2

くりこみ群フロー
変数： wA ⌘g2 ⇤ ✏
, f⌘
, w⌘
2
8⇡ A
A A

C|B|
, h⌘ pA⇤<latexit sha1_base64="(null)">(null)</latexit>(f, wA ) = (1, 1)<latexit sha1_base64="(null)">(null)</latexit>

400
200

h

(i)

<latexit sha1_base64="N0Zpz4fDSC2Twg5XGt2UXKfIFio=">AAAFj3ichZTNbtNAEICnAUMJP23KBYlLRFSUSFW0rpCCkIqicim3/pC2UlpVtrttV7HXW9tJm1p5Ae6IAxIIJA6Ix+DCC3DoIyCOReLCgdmx6U+i2Gt5PTueb2Z2Z3dt5YowYux0onDtunHj5uSt4u07d+9NTZdm1kO/Gzi85fiuH2zaVshdIXkrEpHLN1XALc92+YbdeaH/b/R4EApfvor6im971r4Ue8KxIlS1q0dzB7WFKptjtZ3pCqszauVRwUyFCqRt2S8VGrAFu+CDA13wgIOECGUXLAjxaYMJDBTqtiFGXYCSoP8cBlBEtotWHC0s1Haw38dRO9VKHGufIdEORnHxDZAswyz7wb6wM/adfWU/2d+xvmLyoXPp49dOWK52pl4/WPuTS3n4jeDggsrMOYI9eEq5CsxdkUbPwkn43snbs7Vnq7PxY/aJ/cL8P7JT9g1nIHu/nc8rfPVdRj425jJ+xWKMzHGGEq1UaidRc0Sr5tE8JNYppmoJ9DC4JCuqVx+lCPuL2ozzEECPeC3rvMpUk2zmOGUSIsZxHnE4FOMwl9jFJ4mh1/0Y+5g02VRrhGnlMp2h2XRyCTVEqFxicYhYzCVOUH+VYedMQDtxlNs6z+//6bRwB2TH0efycpREY9MuyounrV2y5rTTJN0bgvxVifNT2zj14OGeHECN/BbxhjKH76NRYX2+brK6ufKk0lxK76pJeAiPMIIJDWjCEixjlXVmb+A9fDBKRsN4bjQT08JEytyHK814+Q/6lC2c</latexit>
sha1_base64="OFVshI1l5/jxnIN+Oo85aM2dmFE=">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</latexit>(w, h) = (0, 0) の固定点

0
-200
-400
0

200

400

600

800 1000wh<latexit sha1_base64="(null)">(null)</latexit>

w のフローが支配的モデルA

動的ユニバーサリティクラス
C=0

C≠0

モデル E (xyモデル)
固定点(i)

モデル A (イジングモデル)
固定点(iv)M. Hongo, NS, N. Yamamoto (2018)

C : カイラル磁気係数

カイラル磁気効果がユニバーサリティクラスを変える
モデルE

2成分秩序変数 + 保存電荷↵
<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>

保存電荷ʼnA [ ↵ , nA ] 6= 0
<latexit sha1_base64="(null)">(null)</latexit>

モデルA

2成分秩序変数

保存電荷

nA

↵

<latexit sha1_base64="(null)">(null)</latexit>n<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>

カイラル磁気波<latexit sha1_base64="(null)">(null)</latexit>n [ ↵ , n] = 0<latexit sha1_base64="(null)">(null)</latexit>

まとめ• カイラル輸送現象を考慮したQCDの臨界ダイナミクス
磁場中のカイラル2次相転移の動的ユニバーサリティクラス
C=0

C≠0

モデル E (xyモデル)
固定点(i)

モデル A (イジングモデル)
固定点(iv)

Masaru Hongo, NS, Naoki Yamamoto, JHEP 1811, 108 (2018)

カイラル磁気効果がユニバーサリティクラスを変える• 他のトポロジカル輸送現象と動的臨界現象？