sm-q3-04 - PHY 4523 NAME and (Last-4 UF ID Number):...

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Unformatted text preview: PHY 4523 NAME and (Last-4 UF ID Number): “Statistical Physics” Spring 2004 | Quiz 3 (5 points) 30 January 2004 / Professor Mark W. Meisel ’ (D PLEASE PRINT and box final results. Show all work for full credit. Work must be clear and unambiguous for credit. Consider a set of Ising spins as discussed in class and in the textbook. The spins are noninteracting, have a magnetic moment u, and are in an external magnetic field B. Show that the magnetization M is given by u(n+ - 71—) MN (MB) M = —— = —— t h — V V an kBT ’ where the notation is the same as the one employed in class and on the formula sheet. 01’ M _ _ In? "LL nlr‘F‘A-‘N New? Ska [aw 6='/415)ml$ wt? \ \IoQ A ‘g ‘a. 4‘ is a we c my all g f #OQWY‘ 40cm” M 3?“, Mgr 0+ u? 69* g ‘3 ‘ ha ”“ (sigma com-m Mm) N~w+ 4. L.. up: $464.9 Wrath ,7 3; - - kg {N (All MU (hint/{$121+ ‘ (Nan) [A nu \ :1” “21"le _ .l S? I“ hh §Ntflu‘4+‘kn4 —(N-Af\ln(U—nj§ SI: 4“ kgflgi [WM‘ %{nfl* —([_ i" (N‘VM all i “LEW; AT: l“ U E ’50 ._— fl 5' AME 3* («u_%(“* _nt :(uMi-ilnu— {-14. A Sr-hwi mu 1+ - at ( “W” "A? N N (l‘w\\~’\~+(l_‘g~)lh[(U—M+‘] ‘uflfi>+ (1-13; 1% (Na/mfg N gllhbog 9,; M‘s; +(t~flg)lm(l-%Bl [9‘ "L‘- ‘_ (if) "M N l as y = ‘M'; @ ‘ am! fls-n*e+ (M—nAe: Ue—2n+e ... —~ ( + ‘ ynu§_%fim(%)+9?le¥% 'Cm ciusns—Mau. Hm“; mii=¢cmfihmkmk 3S => {p (5-H: gag): (3.: t as » fi=‘uN§L\(fl wwz L 2 A z) + .7: (RA 2 ‘ L l— . \vx l (I'X) Z » i 1 ( M" TGEH'B = ,Mk 7?3M(%-M(fl : k3” ‘7 “(53 a» ‘L \ EB (“X T‘ '5; (“C 7") 2e _ _ we (LBT - (a 19/1»? _ Q ‘ '75; a .2: 5 #31“ “Me? * l-r ez+¥ejificr ? x(€+‘\= Ive:i ’ (l-c‘) (Ci-t8 f T (CH6) (Cum “‘Jmuki So ;i H (M, “_\:[CL‘{\, (figlu = -><~.= quC-é-3 [31' lg: MB] AOM—"A’B ...
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sm-q3-04 - PHY 4523 NAME and (Last-4 UF ID Number):...

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