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?

-

blank.

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

blank.

• 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

blank.

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)

blank.

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 .

blank.

(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 .

blank.

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 .

blank.

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

blank.

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 .

blank.

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 )