量子相变和量子临界现象

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书书书 !29!4# 2009$12%& ’ ( ) *PROGRESSINPHYSICSVol.29No.4 Dec.2009 !#$:10000542(2009)04032527+,-#:20090901./01:23456(./(789:10424401,10674058,60876065):23;.=?@A(789:2006CB921803,2009CB929504)BCDEmail:gjin@nju.edu.cnEFGH:EFIJKL!#,$ %(MN(OPQRS23;TUVW:&’X,MN210093)%&: YZ[\]^_&’(‘BEFGH:EFIJKL,abcdeGH‘fgEFhiBjkl,mnopqIsingrstueEFGHB.Yvw;xyz{|}IJKL,~eEF:EF;B.Y:;5EFIJKLB,e、:B/PGH;EFIJlB;F&、¡¢&:£⁄¥pPƒ§¤'BG“«‹FX›;fiflEFT、–†‡·:¶•‚„”,tueEFIJlg»…:†‡X›?‘B。’():EFGH;EFIJl;;;;/PGH;FX›*+,-$:O48 !./01:A0 &’g‰]^_&’(‘¿`´;ˆB&’˜¯˘,g˙¨:¿˚¸B`}HE(˝、˛ˇ—pq)By,¿X›BkEfi»B._。´K,‰ƒGEB,._B。ƒÆ,ªg{˙¨By,ŁgƒEØŒHB¿¸ØeGH。¿ºz,ƒ˘EFGH[1~6]。:¨B}GH,EFGHBØ˘æ\X›.YG“BEBı。ƒłø,¿X›BGHœßæ¨BŒH,˘X›BHamiltonE‘BE!¸。#$,GHØg%&E(˝、˛ˇ—pq)B¿v¸BIJ。X›B’BEF._(ƒIJ)。¿*+,~-BvT˘EFGH‘fg.BIJKL。ƒ/EFIJKL{]^_&X›,v0˘G“«‹FX›B&’l1z;ˆB,23˘!¸lB。4’EFIJKLB5ˆ’678˘}IJKL‘´B’6:;9:B;。2=Z‘?{EFGH:EFIJKL@tu[7,8],5YZA{B*+X›B[\。YZB5ˆ=C„gDE‘B《]^_&’(》yB¿F。—GHƒ¿5¯g]^_&’(*‘B;ˆl,IAJ’b#Æ,KL)(MJB;N。EFGH:EFIJKLOP]^_&’(‘QR:GSB&’=C,ˆ{TU4Btu,AVWæ—BkX:YZ,[\]—7^_。1 ()*+‘Q#azb,¿X›BEFGH˘_g˙¨yƒX›BHamiltonE‘BcŒH~dBGH。‰enIJT,EFX(B._ØŒH。:W¨GHG*,˙¨GH5ˆ˘KEFhi„‘fB。gE„-g@hiB}GH‘[9],EYjjK˘EFB,*gklˇ—kmB,n˘{GHGBopq„d5lBr˘EBs}tu。1.1 2345678gv»¨y¿&’X›BGHnw‘EFlk(xN。EFGH´(y˙¨GH,nz{-|},ƒ/~˘¿VW&B:JB#T。»¨23˙¨yBGHjK˘EFBzjk˘sB,ƒ!æEF:shi5l[6]。U$,˙¨vWYjœGHBEFhi。)¿,æ˙¨Bjl,˙¨y`}HEBH~dBGHœkgUBUV‘(#d。n˘,»¨KPv»¨GHjKgUV$(#d,œk„˙¨IJKLƒ¿vW。›@&’(‘¿.YrsBq„œg˙¨vWEFhi,˘sIJq„B。ƒg¿ØGHBv¸˘’B,z˘},wg˙¨vWBÆKYjœGHlBEFhi。g}IJKL‘[10~12],¿`´;ˆB&’E˘}tuBo,ξ(犜)=ξ0狘τ(犜)狘-ν(1)‘狘τ(犜)狘=狘犜-犜犮狘/犜犮¸eGHKLØBIJT,ν˘IJ_c,ξ0˘@B˙¨o。g¡,oξ(犜)¢\sKL。oξ0œ˘¿£⁄E,¥kg8PB]^&X›‘(˚¸;nƒ˝%,ξ0ßæX›B=§c,v0˘IJ¨犜犮。„eS¤«‹FX›BEFhi,gjKdeBroglie}poλ(犜)=2π犺2犿犽犅()犜θ=λ0犜-θ(2)‘λ0=(2π犺2/犿犽犅)θ,θ˘}po_c。m´y,θ=1/2,n˘„e'C@jkBEF›@rs,g¢“¸θ>0。«gAb,θ=1/狕,‘狕˘¿X›BX(IJ_c[13]。c犿jKÆ‹FBUEˇ—˘‹'›G“B¤‹FBhE。fifl,pcB–†{GHT‡B}X(KPGl1zEFhiB·,jK¶•¿δ=λξ>1(3)gZ‚GHT犜犮‡,„”(3)BGHjK(yEFGH。ƒfi»˘Suzuki…B[14]。ƒ‰Z[9]‘„lEF¿œ¨@B§,ˆ`}poλknZ´‹Fˆ犪。U˜$,ƒ¯B˘¿.Y#B˘xRfi。ƒ.Y#~„,GH˘¿/#KL,g˙¨æstuBoξB˚=ØBKL˘GB。¥(3)gIJT(„”,EFIJBq„¸Ø。(3)…eØEFGHBˆ˝˛。EFIJKL,ˇ—}“GHT”BEFhi,Eg]^&X›‘…K。‰ˇH¨犜犮>0,—(1):(2),g犜→犜犮,ξ→∞,n˘λ5˘WB。@KIJT犜犮B(狘τ狘→0)˘ÆK…sq„。(3)KP(1):(2)Æ,jKb,EFIJKLjKØ,z˘}EFhiAW¨IJ狘τ(犜)狘1,¥ˆ„”犜犮(ξ0/λ)1/ν<狘犜-犜犮狘犜犮(4){æ犜犮>0,ƒ(U¸,zj;˙¨vW犜犮→0,¥ˆ犜→0,K狘τ狘1ƒ。,fiξ0(犜犮)<λ(犜)(5)(4)¸BGHBEF˘fgB。ƒjK(E˛犜θ<λ0/ξ0(犜犮)B。g?fl,ßæ¿v¸X›B`£⁄l,»¨IJq„jK˘EFBˇsB。¿º,gjK“¸,s¨、s»¨:EFBIJlS˛eIJq„B/§s。ƒ/IJKL§s!¸æ}poλ¨yλ<ξH”»¨yλ>ξ,3¿IJlBŒH,5。v0˘fgs(δ<1):EF(δ>1)BÆ,ƒ/Æ\es¨KL:犜→0EFIJKLB。—«B6,{æª&’X›ˇ›@rs,g3’E&gBGH。¿˘¨犜,¿˘`}E,ƒ¯犡Æ。B,gƒ,\oξ¢ßæ¨˘ŁB,U$zßæc犡,@Kξ=ξ(犜,犡)。}X(EKPBGE{犡BßlØ{犜Bßl¿Œ(cº)。˘,…Kg犜犮(犡)ˇ—犡犮(犜)BGHjgO¸B犡yŒH犜(犜GH)ˇ—˘O¸B犜yŒH犡(犡GH)zƒ。¿ºz},犡GHBl:犜GHBlB,nfgøGiBj§*l。g(4):(5)‘,犡犜KP犡犮犜犮,gjK—HE犡æØB。ƒ/˘xƒ…oξ(犜,犡)BX,ƒ:g¨˝犡~0‰犜GBGH˘¿ŒB。¢B0˘,E{æτ(犜):珓τ(犡)BXBIJ_c¨623& ’ ( ) *!29 ¿º˘B。’jK“¸,gcdτ(犜):珓τ(犡)Bq„_ciG。‰5ı犜犡{iBX‘B¿l˘fgB。n,e`´vłB,gzk_\ŁB{iX,'øœ4BIJ_cKPß,v0˘}poλ(犜),{犡GHœ§*&。1.2 9:Ising;opq‘BIsingrs˘EFGHBfi¿Brs。deGennes˘!¿g!4#LyAƒ/rs~)z?g¿$%&‘¥X›BˇH˜¯B,*{’()*(KH2PO4ˇKDP)[15]。HamiltonE„犎=-犑∑犻犛狕犻犛狕犻+1-犎∑犻犛狕犻-Γ∑犻犛狓犻(6)‘犑„fi4B–E,犎„+狕,Bpq,Γ„-˘æ狕,Boq。(6)@\Brs˘sIsingrsB¿;ˆBR[16],mnoqˇ˘./0eEFtu。‰4gWBˇH¨jKK,ƒBIJq„VoqEFhiB·,ƒT‰sBIsingrs˘GB。n˘‰犜=0,oqgIJΓ犮4GH。ƒ/EFGH˘æX›._B01ŒH2˛B。g犜=0,‰Γ→Γ犮X›BIJq„‰犜≠0sBIJq„˘ŁB。”,sB¿…IsingrsfgGH,ngjKK,oqIsingrsg犜=0˘fgGHB,˝jK3˚`4。Pfeutye¿»#B’64’[17]。gcº(6)‘犎=0:犑O¸Bfi¿。‘&’Baz}5U,g犜=0’Z6T:¿T˘Γ=0,BX›fgowp,E〈犛狕〉>0;7¿TgΓ=∞4,æoqBfg89eowp,BE〈犛狕〉=0。„Γ=0:Γ=∞B:¸T0˘G:GB,~F。BgjK~„,fi%;Γ,gIJΓ=Γ犮4,fg‘G〈犛狕〉>0G〈犛狕〉=0B˙¨GH。gΓ犮‡,‰}IJKL§,gjK¿z\EFIJT(QCP)BIJ_c。Hertzgs6Z‘…:Re{«EFIJKLB;ˆ::[18]。‘EFX(BY$zb,EFGH˘!¸X›lB’{=ıBG{˝HlB。U˜$,jK?@,{æKgBrs,EFGH˘oqΓ‰–E犑Bı~dB。B,cº*@Γ/犑z\˙¨‘G〈犛狕〉≠0G〈犛狕〉=0BˇH˘’B。‘;9’6B#Tzb,GH‰gΓ/犑=(Γ/犑)犮y:B˙¨TBfg˘XB。XæEFIJT,gjK¿IJ_cz\B&’EgGHTBABq„。mn;9H,grjKƒg«?B’T04æΓ/犑=0:Γ/犑=∞BRfi。oq‘BIsingrsjKUVzU。¿ssBŁ˘CFDPLiHoF4。ƒ/EFPB»¨plgQ#˙y?(?ƒ。fiGBvw˘,g¨»æ2KX›‘¥4æ+3BHoCF$844,BHoCFB4mnpHvG“ØI。ƒ4B,m´‰DJB,¿,_,¥,$:,y。ƒ/gKT$B4LMjKIsingrsz\。g7pqBy,X›B._˘˛vB¥pG:@B4N,$ˇN,y。!#!$%&%’%%!!#%$%’%#%!!$%&’!#$#()*+,-#1 æLiHoF4B¨‰opqBUVOEG#。~4Z[19]#1˘æLiHoF4plBUVOERfiB#,‘P0„¨犜:pq˝Γ。GgW¨GHQK=。ƒQRRæEFGHT,gEFGHT4¥p¢EFtuz89。g7pq、˙¨,X›A˘ŁBG,gW¨A…KEB4Øˇ。z˘},fiDPg{˙@B4N,$,}tuA~d¿4Bˇ,y,5。Sø¨BT,c4Bc1U«,˘4,$‰,yBc1G。ƒ˘V›B}tu~BGH723 !4#/2W:EFGH:EFIJKL  nw。{æLiHoF4,Ø¥pG,XpGBˇHBIJ¨Y„1.5K。LiHoF4B¿ZA

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