Документ взят из кэша поисковой машины. Адрес оригинального документа : http://shg.phys.msu.ru/educat/vinogradov/Lesson5.5.pdf Дата изменения: Wed Mar 12 16:11:34 2008 Дата индексирования: Mon Oct 1 20:47:18 2012 Кодировка: Поисковые слова: m 1

, , . . . , . . , . . , , ( ), .


. ) T, Tc , =Tc. , Tc , m ~(T - T ) c


h T= Tc , = Tc m h. h m ~ h1/

(630 ) 627,56 , 629,43, 631,30


= ( m / h )T T h=0, (T - Tc ) - T > Tc = (Tc - T ) - Tc > T


T h=0, (T - Tc ) C= (Tc - T )
- -

T > Tc Tc > T



1 H =- 2


j

vij i j - vij j + h



i h

hi = hi =




j

vij j + h = R


j

vij + h =v ( 0 ) R + h v(q) = -e -e
- h - h


j

vij exp iq (ri - rj

Sp i e i R = = h Sp e i

h

e = e

h h

= th v ( 0 ) R + h

= 1/ 2,

= 1/ 3, = 1


Sp i e i R = = h Sp e i

h

e = e

h h

-e -e

- h - h

= th v ( 0 ) R + h

1 R = th v ( 0 ) R = v ( 0 ) R - R~ 3 ( v ( 0 ) - 1)

( v ( 0))
3

3

R

32

( v (0))

3

~ v (0) - T


m ~(Tc - T )

= 1/ 2


R = th v ( 0 ) R + h = v ( 0 ) R + h -

( v ( 0)
=0

R+h

)

3

3

T = Tc = v(0)
R (1 - v ( 0 h-

))

( v ( 0 ) - 1) ( v (0) = h-

R+h

)

3

3

( v (0)
3

R+h

)

3

R ~ h1/

3 + h ~ h1

=0

/3

m ~ h1/



= 1/ 3


-
H [ ] / T = d x a0 + a2
d 2

( x)

+ a4
min

4

( x)

+ c ( ( x
)/
2

))

2

- h ( x )

P=Z e

-1 - H [

] / T +( -

min

min , = 0 2
min

(

a2 + 2a4

2
min

)

-h =0 a2 > 0



min

h /2a2 = 1/ 2 ( - a2 /2a4 ) + h / ( -4a2

)

a2 < 0


a2 = a (T - Tc

)
= 1/ 2



min

= ( - a2 /2a4

)

1/ 2

T < Tc , h = 0 T > Tc T < Tc

2a ( T - T ) c min = = h 4a (T - Tc )

-1 -1

=1


1 H [q] / T H [q] / T + 2



ql2 / l2 + c ( ( x

H [ ] / T = d x a0 + a2
d

2

( x)

+ a4

4

( x)

))

2

- h ( x )

H [ ] / T =



k

-k

(

a2 + ck

2

)+

a4 k k k

- k - k - k

k
lim k 1 =2 k

-k

1 = 2 ( a2 + ck
-k

2

)

T Tc

-k

lim k
k 0

1 1 = ~ ~ 2 ( a2 ) T - Tc



P = Z -1e Z = e 1 H =- 2
- H [ ] / T

- H [ ] / T


i 2 j



i

J (
ij

i -

) -

ih


P ( q1 , q2 ) q1 , q2 ; q ­ , 1 q = ( q1 + q2 ) 2 q

1 1 P ( q ) = dq1dq2 q - ( q1 + q2 ) P ( q1 , q2 ) = q - ( q1 + q2 ) 2 2 P , q, P ( q ) P ( q1 , q2 ) ; q
q
2

= P(q )dq =

(

q1 + q2

)

2

/4


1 x = d b
P ( ) = e
- H [ i ] / T





i


i ,x

x - b

-d


i

ix
y

e
P

- H b [ ] / T

H

bloc

=b

d



1 2 4 a2 x + a4 x + 2



c ( x -

x+ y

)

2



= ( a2 , a4 , c
H
bloc

)

= K H

= R




* = R * = * +
lin

= R lin
R=

=

*


lim Rs (Tc , h = 0 ) =
s *


Rs (T , h = 0 ) = * + Rslin = * + t1 (T ) s y e1

= (T ) - * =

t (T )
i

ei

R

t1 (T ) = A(T - Tc ) + B (T - Tc ) 2 + ...

Rs (T , h = 0 ) + A(T - Tc ) s e1 ± ( s /
*

y

*

)

1/

e1

1/ = y, = A(T - Tc )


1969 . , s 1. ni = 1, ...., s H Potts =- s J ni n j - 1 - sh ni - 1

(

)

(

)

, .

Z=
sJ



e

-H

Potts

/T

=



( e
sh



ni 1

-1 / T

)



( e

sJ

ni n j

-1 / T

)

e - sJ / T ni n j ( nin j ) = e = e - sJ / T + (1 - e - sJ / T ) nn i ni = n j 1 q = e - Js / T p = 1 - q 0 < p < 1
-1 / T

j

Z=



exp(- H / T ) =


ni i, j

(

q + p

nn i

j

)

sh ( e

1 ni -1 / T

)


, p nn j i q. q z (1 + ( s - 1)e - sh / T ) , z ­ . - 1 + ( s - 1)e - shns / T

,

(

)

Z= =



exp(- H / T ) =


ni i, j

(

q + p

nn i

j

)

( e
sh

1 ni -1 / T

)

=





pq

R

L- R

(

( nh

))

N

n

R --

(

L - R ) --
- sh / T

= (1 + ( s - 1)e

)


,
ln Z K ( x ) = lim lim = L s 1 L ( s - 1)



ne

- Nn h / T

, ln ( ( nh

(s-1),
- nh / T

N n ( s - 1)e - nh / T N n ln(1 + ( s - 1)e e ) ~ ~ ~ e L( s - 1) L( s - 1) L( s - 1) L Nn n ~ L
n

))

N

- nh / T - nh / T N n

e

- nh / T

P( p) = p -



n n = p + K

h=0


. z=6

. z=4

zpc ~1