Конспект лекций по статистической физике. Коренблит С.Э - 144 стр.

                                     |144|
                                                      0               1
  kT @ ln QH =) kT X @ ln Q() =) X B X @ @ ln Q()             p A =) (14.18)
   V @H           V = @ H              = V p @ (  ) ;V       
       X X B X  ("p  )np X B X X 
  =)                     np e            =                       np wnp =) (14.19)
      = p V Q()   
                p np =0                     =   V   p     
                                                          np =0
         X                                                     
  =) B <> <> = B <> <> =) M; (14.20)
       V p                             V
{ ¨ ¥áâì ­ ¬ £­¨ç¥­­®áâì, ª ª á।­ïï ¯à®¥ªæ¨ï ¬ £­¨â­®£® ¬®¬¥­â
¥¤¨­¨æë ®¡ê¥¬ ­ ­ ¯à ¢«¥­¨¥ ¢­¥è­¥£® ¯®«ï ¢ á¨á⥬¥, á®áâ®ï饩 ¨§
¤¢ãå ¯®¤á¨á⥬ (14.6), { á <> ç áâ¨æ ¬¨ á ¯à®¥ªæ¨¥© ᯨ­ +1/2 ¨
娬¨ç¥áª¨¬ ¯®â¥­æ¨ «®¬ + =  + 
 ¨ á <> ç áâ¨æ ¬¨ á ¯à®¥ªæ¨¥©
ᯨ­ 1=2 ¨ 娬¨ç¥áª¨¬ ¯®â¥­æ¨ «®¬  =  
.
    ‚ ¯à¨¡«¨¦¥­¨¨ á« ¡®£® ¯®«ï: 
 = B H  kT , à §« £ ï J0( ) ¢
(14.15), ¢ àï¤ ¯® á⥯¥­ï¬   =  
, ¨ ®£à ­¨ç¨¢è¨áì ª¢ ¤à â¨ç-
­ë¬¨ ¯® í⮩ à §­®á⨠童­ ¬¨, ­ 室¨¬:
                   0          1                   0 2           1
                    @J 0 ()                  1
 J0( )  J0() + @ @ A ( ) + 2 @ @2 A ( )2 =@ J 0 (  )
                     0          T;V
                                1               0 2         1 T;V
                       @J ()                1 @ J ()
          = J0()  @ 0 A B H + @ 0 2 A (B H)2: (14.21)
                          @ T;V             2 @ T;V
®¤áâ ¢¨¢ (14.21) ¢ (14.15), ¤«ï à áᬠâਢ ¥¬®£® ᯨ­ S = 1=2 ­ ©¤¥¬:
                             0 (1=2) 1
                               @
          JH ()  J0 () + @ 0 2 () CA
                           1     2J
           (1=2)    (1=2)    B                            (B H)2:         (14.22)
                                   2      @        T;V
Œ £­¨â­ ï ¢®á¯à¨¨¬ç¨¢®áâì, ª ª ¯à®¨§¢®¤­ ï ®â M ¯® H, ᢮¤¨âáï ª:
            !           0 2 1                       0 (1=2) 1
        @
 T = @ H M      =    1 @ @ J H  A   =)1     1   2   @ 2J      ()
                                                    @ 0 2 CA ; (14.23)
                                                    B
             T;V      V @ H T;V S= 2 V
                              2                   B        @         T;V
                    0         1                          0             1
                  1 @ @J0 () A             (1=2)           @n (T;  )
  ,â ªª ª n=                       ; â® : T = 2B @                   A : (14.24)
                  V @ T;V                                     @ T
‚ëç¨á«¨¬ @n=@ ¤«ï ¢ë஦¤¥­­®£® ä¥à¬¨{£ § : T  TF : ‚ᯮ¬¨­ ï
¢ëà ¦¥­¨ï ¤«ï ᦨ¬ ¥¬®á⨠(9.10), (9.11), á ãç¥â®¬ (13.39) ¨«¨ (13.40),
¢ ᮮ⢥âá⢨¨ á (13.52), ¢ ᨫã n(T; )  n (T; P (T; )), ¯®«ã稬:
                                                  2                 3
      @n ! = n @n ! = n2K (T; n) =) 3 n 41 2 kT !25 : (14.25)
                               T
      @ T       @P T                      2 0         12 0