blank. j[§gxx 7) · blank. • i > = it - - t¥ - - i> tz is unstable to coupling to any...
TRANSCRIPT
blank.
Hard Problems : transverses- Isvythodel .
Hiram = -J[§gXx - E,#7)① symmetries : ✓• S -- IX. [ Harm
,s ) -0 .
2h : 5=1 . { X×Xy,7×7-7=0 .
• translationsome .-
@ limits .
±⇒Hgs = - EX .
X. Its > = -111 go > fx
⇒ Igs? = ¥0 I→?
Fix.¥'sSlgs } -- Igs), = It > + IT >
"
paramagnet ?X
- H?
-
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goo Ho = - J §Z¥+ .
It > = It . - - T >,I -7=11 -
- - D.
SII > = IF > .
Not symmetric .
I 7 = # ( it > ± I -s )^
SI 5- * I
eirene : if you and VLA
then I + ) 5 the groundslate !
But Degenerate fatty : It .SH = - § GJ XxhF-
Q: GI (SH) It> to?
-
requires n-- V !-
T =L - I @Hilt> a o.
- e-VK.hu
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• I > = IT . - -T¥ - - I >Tz
is unstable to coupling to any environment
→ It . . . T ) or Id ---t ?
.
• Add a longitudinal field SH = - fh×Z×=
explicitly breaks S .
-
E'S,SHI -- o .
-'→ tvh
,
N⇒ .
- It > p-
him bin Igs> # tying; ImN-so h⇒ it
e
-= It>
=L
pSSB harms physics !in the thermodynamic. -
limit .
=
spontaneously breaks
Hg. . 5 a ferromagnet kklspi symmetrybut
-preserves lattice symmetries
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FERROMAGNET PARAMAGNETTttTt →⇒→→→
#gHtt Gc
tgt? : 2 2222222 ?? ' ' l l l ll 'll 1
Topological = Can't change smoothly .e--
③ elementary excitations specthmqtfy- - Eying 5 Ba - - -
④ H -- toD
eying,wgtX.
%"s¥⇒Notthese
yg%= he→→→7 Eo- 1-state
firsthas Eo= - 85N I→ →⇒
"scifres : In> = It . . .
-say -2- - -⇒
nth site
(Ho - E) In> =2gJ In)
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Dgcnpath: Mix In > . by sH= -JEZZ
2- (→> = It) . /ASSuMEd=I
ZjZjt , I -3.5+17=1%-3+17⇒Zjt , hµ=I→
. --→I '' →3=4+17
if 5- h
= It . . . E. I > Hh- I >
if j=n
→ lentil §.
ZjZj+ , In ) = 1 .
Hefflh ) = -J (Inti> + In-D)
PBC : In -iN)=In?+ (Eo -129T) In> .
In > - Tng e-iktilh > 4¥.a
Nam -
- e. .N .
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(H - Eo) Ik ) = ( -2J asha c-zgJ ) ItsC-Chelf
echoes - asha, 29¥Keos +51k¥ . - - e!↳±faI = 2J (g- l) = eneyygei
C- = s + KIp
2M
nest energy M- inertialess
massive= ←Jazj
'
these particles are called spin waves .
In > = Zn Igs,>
2-n'= A .
Thee particles are their ownantiparticles .
blank.
Nvm atm :
§ f-X; )only angered nod 2 .
( Hp:EE .. First. )Mahe g smaller :sg}
#mo??!!// PARAMAGNET- I
g•
partite X g -- I
"condenses
"
= ( at > to .
I creates particle X .
condense spin ⇒ ( Z ) to .
Hips few .
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A 2 - particleT.IE#aunnim .
It I -pahdibmd
18 It? eyaetale g Ho-
- -552-2=19. . -TTT) in Eo = - JN
Excitedstat : Htt . - - tfttttdtlf- W
-15
It . T.f.tt . - T ) -577=+5
= Xj t> .
(H -Edc ) -425+257/7It .
- - t.tt.TNH - Eo) ( t ) -425+2511 ) same!elements exc : doMall . restenergy 2J .
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up PBC,Dw, can only be created in pairs .
perturb by
sHEgXi .
Xj+ , I - - - TTB.
- dit , t . . . d)÷
= I r . - Ttt; Titi.dj→ - i - - - 7-
= 12717
Hey- Eo) II ) = -gJ( him> + Is- D+ 251J > )
→ Egnew( k) = 2J ( I - gashed .
⑤Dpw -
- ash -g) {\ache1=2Abw ÷¥g
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④ Munfheory(41 HIX) 3 Eaetuaegs .
I MFT ) = 14,7×014>④ . . . Xn )"
ansate : . assume Xx = 4 Fx .
in > = ¥017 ?= xp (cos%eik4→ >
+ sin of e-ik I←)),
YA-÷.o -- o -- he is It"
ea←
T
< Till I ti > = cos O{ 9*171 Ti ) = sin @cosy .
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Eloie ) = Lint ftp.mlh )= -NJ ( since as
'
y + gaso)-
recon
may me"' g¥he# o
→ ECO)
g)ge -- Zl:¥÷÷÷ "H.
Approach g→got . O is small .
Eto'
NT f- z t ' oh fo'tIft
. . .
<z ; > aSinon O -- ft JFS%.
O 929 a .
blank.
Note : E (m) = Wr m2 tu m4+ at t . . .
Mr. (7) rig ) * 8¥
Hear transition ) - should be analytic .im
(awhatddifehe? )- even in ms
-m cud
mon.Landau- Ginzburg
as offectue actionAFM WRONG
b PM
|a↳go⑧*wreak
.
"condensateof spin flips
"
×(zI→7)= Xt le >
= -ZX l -57
= -ZI-s )