2RandomInteger@D 1; D Table 8
11
H*13.1*L x:= 2 RandomInteger@D - 1; p@n_D := Table@x, 8n<D; q@n_D := Accumulate@p@nDD; r@n_D := ListLinePlot@q@nDD; p@10D q@10D r@10D 81, 1, - 1, - 1, - 1, 1, 1, - 1, - 1, - 1< 8- 1, - 2, - 1, - 2, - 3, - 4, - 3, - 2, - 1, - 2< 2 4 6 8 10 -2 -1 1 2 r@500D 100 200 300 400 500 -35 -30 -25 -20 -15 -10 -5 Show@Table@r@500D, 820<D, PlotRange fi 8- 50, 50<D 100 200 300 400 500 -40 -20 20 40
Transcript of 2RandomInteger@D 1; D Table 8
H*13.1*L
x := 2 RandomInteger@D - 1;p@n_D := Table@x, 8n<D;q@n_D := Accumulate@p@nDD;r@n_D := ListLinePlot@q@nDD;
p@10Dq@10Dr@10D
81, 1, -1, -1, -1, 1, 1, -1, -1, -1<
8-1, -2, -1, -2, -3, -4, -3, -2, -1, -2<
2 4 6 8 10
-2
-1
1
2
r@500D
100 200 300 400 500
-35
-30
-25
-20
-15
-10
-5
Show@Table@r@500D, 820<D, PlotRange ® 8-50, 50<D
100 200 300 400 500
-40
-20
20
40
fig1 = ListPlot@Variance@Table@q@10 000D, 81000<DD, PlotStyle ® YellowD
2000 4000 6000 8000 10 000
2000
4000
6000
8000
10 000
fig2 = Plot@x, 8x, 0, 10 000<, PlotStyle ® RedD
2000 4000 6000 8000 10 000
2000
4000
6000
8000
10 000
Show@fig1, fig2D
2000 4000 6000 8000 10 000
2000
4000
6000
8000
10 000
H*13.2*L
x := 2 RandomInteger@D - 1;p@n_D := Table@8x, x<, 8n<D;q@n_D := Accumulate@p@nDD;r@n_D := ListLinePlot@q@nD, AspectRatio ® 1D;s@n_D := ListLinePlot@q@nD, AspectRatio ® Automatic,
PlotRange ® 88-Sqrt@4 nD, Sqrt@4 nD<, 8-Sqrt@4 nD, Sqrt@4 nD<<D
2 Chapt13.prob.nb
p@10Dq@10Dr@10D
881, 1<, 81, 1<, 8-1, 1<, 8-1, 1<, 81, 1<, 8-1, 1<, 8-1, -1<, 8-1, 1<, 8-1, -1<, 8-1, 1<<
88-1, 1<, 80, 0<, 81, 1<, 80, 0<, 8-1, -1<, 80, -2<, 81, -1<, 82, 0<, 83, 1<, 82, 0<<
-1.0 -0.5 0.5 1.0 1.5 2.0
-6
-5
-4
-3
-2
-1
r@5000D
-40 -20 20 40
-20
20
40
60
80
100
Chapt13.prob.nb 3
Show@Table@s@5000D, 820<DD
-100 -50 50 100
-100
-50
50
100
4 Chapt13.prob.nb
fig0 = ParametricPlot@Sqrt@2D Sqrt@5000D 8Cos@tD, Sin@tD<, 8t, 0, 2 Pi<, PlotStyle ® RedD;fig1 = ListPlot@Table@q@5000D@@5000DD, 81000<D, AspectRatio ® 1D;Show@fig1, fig0D
-200 -100 100 200
-200
-100
100
200
H*13.3*L
H* def *LH* Nearlest Neibher *Lnn@f_, p_D := Table@f@@Mod@i - 1 - p, NND + 1DD + f@@Mod@i - p, NND + 1DD, 8i, 1, NN<D;H* p = H0 or 1L for Heven or oddL site *LSeSo@f_, g_D :=
Table@If@EvenQ@iD, g@@Mod@i � 2 - 1, NND + 1DD, f@@Mod@Hi - 1L � 2, NND + 1DDD, 8i, 1, 2 NN<D;H* Heat Bath Method ; spin = 2Hn-1�2L = 1,-1 ; n=1,0 *Lhbm@f_D := Table@RandomChoice@
8E^HBB 2 Hf@@iDD - 1LL, E^H-BB 2 Hf@@iDD - 1LL<® 81, 0<D, 8i, 1, NN<D;
H* initial data *LNN = 30;BB = 1;Mag = 8<;Se = Table@RandomInteger@D, 8NN<D;
Chapt13.prob.nb 5
Do@8nnSe = nn@Se, 0D; So = hbm@nnSeD;nnSo = nn@So, 1D; Se = hbm@nnSoD;S = SeSo@Se, SoD;Mag = Append@Mag, Total@SD � NN - 1D
<, 8500<D
ListLinePlot@MagDArrayPlot@8S<D
100 200 300 400 500
-0.8
-0.6
-0.4
-0.2
0.2
0.4
0.6
H*13.4*L
H* def *LNN = 2 MM;nn@s_, p_D := H* p=1 or 0 for even or odd *L
Table@s@@Mod@i - 2, NND + 1, Mod@j - 1, MMD + 1DD +
s@@Mod@i - 1, NND + 1, Mod@j - Mod@i + p, 2D - 1, MMD + 1DD +
s@@Mod@i - 1, NND + 1, Mod@j - Mod@i + p, 2D , MMD + 1DD +
s@@Mod@i , NND + 1, Mod@j - 1, MMD + 1DD, 8i, 1, NN<, 8j, 1, MM<D;
SeSo@f_, g_D := Table@If@EvenQ@i + jD, f@@i, Ceiling@j � 2DDD, g@@i, Ceiling@j � 2DDDD, 8i, 1, NN<, 8j, 1, NN<D;
hbm@s_D := Table@RandomChoice@8E^HBB 2 Hs@@i, jDD - 2LL, E^H-BB 2 Hs@@i, jDD - 2LL< ® 81, 0<D,8i, 1, NN<, 8j, 1, MM<D;
H* magnetization *Lmagnetization@B_D := H
BB = B;
Do@8nnSe = nn@Se, 1D; So = hbm@nnSeD;nnSo = nn@So, 0D; Se = hbm@nnSoD;S = SeSo@Se, SoD;Mag = Append@Mag, Total@Total@SDD � HNN MML - 1D;
<, 81000<D;ListLinePlot@MagD
L;
H* initial data *LClear@Se, So, S, MM, BB, kkDNN = 30;MM = 15;
Se = Table@RandomInteger@D, 8NN<, 8MM<D;Mag = 8<;
6 Chapt13.prob.nb
magnetization@0DArrayPlot@SD
200 400 600 800 1000
-0.05
0.05
Chapt13.prob.nb 7
Se = Table@RandomInteger@D, 8NN<, 8MM<D;Mag = 8<;[email protected]@SD
200 400 600 800 1000
-0.6
-0.4
-0.2
0.2
0.4
8 Chapt13.prob.nb
Se = Table@RandomInteger@D, 8NN<, 8MM<D;Mag = 8<;[email protected]@SD
200 400 600 800 1000
0.80
0.85
0.90
0.95
Chapt13.prob.nb 9
200 400 600 800 1000
-0.90
-0.85
-0.80
-0.75
-0.70
H* B = 0 to 1 *Lkk = 0;Se = Table@RandomInteger@D, 8NN<, 8MM<D;Mag = 8<;Do@8
kk = kk + 1;BB = kk � 1000;nnSe = nn@Se, 1D; So = hbm@nnSeD;nnSo = nn@So, 0D; Se = hbm@nnSoD;S = SeSo@Se, SoD;Mag = Append@Mag, Total@Total@SDD � HNN MML - 1D;
<, 8800<DListLinePlot@MagD
10 Chapt13.prob.nb
200 400 600 800
-0.2
0.2
0.4
0.6
0.8
1.0
200 400 600 800
-1.0
-0.8
-0.6
-0.4
-0.2
0.2
Chapt13.prob.nb 11
