Конспект лекций по статистической физике. Коренблит С.Э - 43 стр.

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â.¥., ¯à¨ Emn =) E1m + E2n  x + y, ¯®«ãç ¥¬ ¢ëà ¦¥­¨¥ ¤«ï ª®­áâ ­âë:
            const 
                    Z 1 ( )Z 2 ( )
                          1      2
                        Z ( ) = exp [x(
                         1+2                  1) + y(     2 )] ;

çâ®, ¢ ᨫ㠯ந§¢®«ì­®á⨠x; y, ¢­®¢ì ¯à¨¢®¤¨â ª (4.25).

3       Š¢ §¨ª« áá¨ç¥áª¨© ¯à¥¤¥«
   ®¢â®àïï à áá㦤¥­¨ï x3.3, ¬®¦­® ¢ ª¢ §¨ª« áá¨ç¥áª®¬ ¯à¨¡«¨¦¥-
­¨¨ ¢­®¢ì ®áãé¥á⢨âì ¯¥à¥å®¤ ®â áã¬¬ë ¯® á®áâ®ï­¨ï¬ ª ¨­â¥£à «ã ¯®
­¥¯à¥à뢭®¬ã ᯥªâàã í­¥à£¨© (4.18){(4.22), ¨ ¤ «¥¥, { ª ¨­â¥£à «ã ¯®
ä §®¢®¬ã ®¡ê¥¬ã. à¨ í⮬ ª¢ ­â®¢®¬¥å ­¨ç¥áª ï ­¥à §«¨ç¨¬®áâì ç -
áâ¨æ ¢­®¢ì ¯à¨¢®¤¨â ª ⮬ã, çâ® ª®­ä¨£ãà 樨 ⮦¤¥á⢥­­ëå ç áâ¨æ,
¯®«ã祭­ë¥ ¢ १ã«ìâ ⥠N ! ¯¥à¥áâ ­®¢®ª íâ¨å ç áâ¨æ ¢ ª®®à¤¨­ â­®¬
¯à®áâà ­á⢥, ïîâáï íª¢¨¢ «¥­â­ë¬¨ ¨ ¤®«¦­ë áç¨â âìáï § ®¤­ã.
®í⮬ã, ¢ ᮮ⢥âá⢨¨ á (3.4), (3.39) ¨ (3.18), (3.31), (4.18), ¯®áª®«ìªã,
 ­ «®£¨ç­® (3.39), ¤«ï «î¡®© ä㭪樨 F (E ) ¨¬¥¥¬ (á¬. § ¤ çã 9.2):
 X                Z1                          Z
    m
        F (Em ) () F (E )D(E; V )dE                  F (H (X ))d ; £¤¥,   (4.27)
                  0                         fX g
                                              Z                  
 ᮣ« á­® (3.19), (3.20): D(E; V )                    H (X ) E d ; â®:   (4.28)
                                            fX g
                               ) %N (X )d = exp [ qs:clH (X )] ds X ; (4.29)
                                                                 2s
 w(Em)g(Em ) () w(E ) (E; dE ) *
                                               ZN           N! h
               Z1                    Z                  d 2s X
 ZN () ZN = e D(E; V )dE  exp [ H (X )] N ! hs ;
         qs:cl      E                                                 (4.30)
                      0                       fX g
£¤¥ s = N d, ¨ d { ç¨á«® ¯à®áâà ­á⢥­­ëå á⥯¥­¥© ᢮¡®¤ë ç áâ¨æë.
‘âண® १ã«ìâ âë (4.29), (4.30) ¯®«ãç îâáï à §«®¦¥­¨¥¬ ª¢ ­â®¢®© áâ â-
á㬬ë (4.23) ¢ ¯à¥¤áâ ¢«¥­¨ïå ⨯ (2.19) ¯® á⥯¥­ï¬ h ¯à¨ h ! 0.
   «®â­®áâì à á¯à¥¤¥«¥­¨ï à §«¨ç­ëå §­ 祭¨© B «î¡®© ¤¨­ ¬¨ç¥-
᪮© ¢¥«¨ç¨­ë b(X ) ¢ à ¢­®¢¥á­®¬ ¬€ªà®á®áâ®ï­¨¨, å à ªâ¥à¨§ã¥¬®¬
ä §®¢®© ¯«®â­®áâìî %N (X ), ¤ ¥âáï á।­¨¬ (1.29){(1.30) ¢ ¢¨¤¥:
                                  Z                    
           f (B ) =  B b(X )      =           B b(X ) %N (X )d :         (4.31)
                                       fX g