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Apéndice E
Programa: Modelo de Ising en Tres
Dimensiones
5 CLS :SCREEN 0
10 PRINT "
*********************************************"
20 PRINT
30 PRINT
40 PRINT "
3 DIMENSIONAL ISING MODEL"
50 PRINT
60 PRINT
70 PRINT "
MacKeown, Newman and Reid, Jan. 1987."
80 PRINT
90 PRINT "
(C) IOP Publishing Ltd. 1987."
100 PRINT
110 PRINT "
*********************************************"
120 PRINT: PRINT "
Hit any key to continue": PRINT
130 IF INKEY$="" THEN 130
140 DIM M(10,10,10)
150 DIM RE(100),RM(100),QE(1000),QM(1000)
160 UA$="E5F5L3D5L4U5L3BM+5,0P1,1" :REM UPWARD ARROW
170 OUA$="E5F5L3D5L4U5L3BM+5,0"
:REM OPEN ARROW
180 DA$="BM+2,-4R4D5R3G5H5R3U5BM+2,+2P1,1" :REM DOWNWARD ARROW
190 ODA$="BM+2,-4R4D5R3G5H5R3U5BM+2,+2"
:REM OPEN ARROW
200 REM --------------------------------------210 REM ARRANGE TO INPUT QUANTITIES H,J AND BETA
220 REM --------------------------------------230 NEQ=1000
240 NI=1
128
APÉNDICE E. PROGRAMA: MODELO DE ISING EN TRES DIMENSIONES 129
250 SN=30
260 CLS:LOCATE 6,8
270 INPUT " Do you need tutorial help Use upper case everywhere! - (Y/N) ";H$: PRINT: PRINT
280 IF H$="Y" THEN GOSUB 3790
290 PRINT"3-DIMENSIONAL ISING MODEL, NXNXN ARRAY"
300 PRINT"
WITH ISOLATED OR CYCLIC BOUNDARY CONDITIONS":PRINT
310 INPUT "ENTER N ( <=8), ";N:BEEP
312 IF N <=8 THEN GOTO 320
314 BEEP:BEEP:BEEP:BEEP:BEEP: GOTO 310
320 IF N=4 THEN INPUT "DO YOU WANT PICTURES? (Y/N)";L$:BEEP
340 PRINT" RESULTS AT END OF WALK WILL BE OUTPUT TO THE MONITOR"
350 INPUT "DO YOU ALSO WANT PRINTER OUTPUT? (Y/N) ";P$:BEEP
360 INPUT "ENTER J (1/0) ";J:PRINT:BEEP
370 INPUT "ENTER H (1/0) ";H:PRINT:BEEP
380 JJ=J:HH=-H
390 INPUT "DO YOU WANT ISOLATED OR PERIODIC? (ISOL/PERI)";I$
400 PRINT "HOT START/COLD START ? "
410 INPUT "(H=HOT, C=COLD)";A$:BEEP
412 INPUT "INPUT ’BETA’ ";BETA:PRINT
420 PRINT"AT PRESENT NEQ=";NEQ,"WALKS DISCARDED BEFORE EQUILIBRIUM"
430 INPUT "DO YOU WANT TO CHANGE NEQ (Y/N)";B$
440 IF B$="N" THEN 460
450 INPUT "NEQ= ";NEQ
460 PRINT"AT EQUILIBRIUM, SYSTEM IS INTERROGATED EVERY NI=";NI,"MCS/S"
470 INPUT "DO YOU WANT TO CHANGE NI (Y/N) ";C$
480 IF C$="N" THEN 500
490 INPUT "NI= ";NI
500 NT=N*N*N
510 NP=NT*NI
520 PRINT"AT PRESENT TOTAL NUMBER OF INTERROGATIONS IS NN=";SN
530 INPUT "DO YOU WANT TO CHANGE NN (Y/N)";C$
540 IF C$="N" THEN 560
550 INPUT "NN= ";SN
555 GOTO 580
560 INPUT "INPUT ’BETA’ ";BETA:PRINT
570 IF Y$="Y" THEN INPUT "OLD OR NEW STARTING CONFIG?
(OLD/NEW)";T$:PRINT
580 REM ----------------------------------------590 REM
600 REM
N IS SIDE OF CUBE, ARRAY M MUST
610 REM
BE DECLARED OF DIM N+2,N+2,N+2
APÉNDICE E. PROGRAMA: MODELO DE ISING EN TRES DIMENSIONES 130
620 REM ----------------------------------------630 PRINT
640 PRINT:PRINT:PRINT
650 PRINT "
START EXECUTION"
660 PRINT "
---------------"
670 REM -----------------------------------680 REM
690 REM
INITIALISATION
700 REM
710 REM -----------------------------------720 SE=0:SM=0:SS=0
730 S2=0:S3=0:S4=0:S8=0:S9=0
740 SP=0:NN=0:NA=0
750 N1=0
760 IF T$="OLD" THEN 1230:
REM Using previous config. as starting one.
770 IF A$="C" THEN 880
780 REM ------------------------------------790 REM
800 REM RANDOMISING INITIAL SPIN CONFIG.
810 REM
(HOT START)
820 REM
830 REM ------------------------------------840 FOR I=1 TO N: FOR J=1 TO N: FOR K=1 TO N
850 M(I,J,K)=SGN(2*RND(1)-1)*1
860 NEXT:NEXT:NEXT
870 GOTO 970
880 REM -----------------------------890 REM
900 REM
COLD START - ALIGNED
910 REM
M(I,J,K)=+1
920 REM
930 REM -----------------------------940 FOR I=1 TO N:FOR J=1 TO N:FOR K=1 TO N
950 M(I,J,K)=1
960 NEXT:NEXT:NEXT
970 IF I$="ISOL" THEN 1130
980 REM ------------------------------990 REM
1000 REM
IMPOSING CYCLIC CONDITIONS
1010 REM
1020 REM -------------------------------
APÉNDICE E. PROGRAMA: MODELO DE ISING EN TRES DIMENSIONES 131
1030 FOR I=1 TO N: FOR J=1 TO N
1040 M(I,J,0)=M(I,J,N):M(I,J,N+1)=M(I,J,1)
1050 NEXT:NEXT
1060 FOR J=1 TO N:FOR K=1 TO N
1070 M(0,J,K)=M(N,J,K):M(N+1,J,K)=M(1,J,K)
1080 NEXT:NEXT
1090 FOR K=1 TO N: FOR I=1 TO N
1100 M(I,0,K)=M(I,N,K):M(I,N+1,K)=M(I,1,K)
1110 NEXT:NEXT
1120 GOTO 1200
1130 REM ***********ISOLATED CONFIGURATION**************
1140 FOR I=1 TO N: FOR J=1 TO N: M(I,J,0)=0:M(I,J,N+1)=0
1150 NEXT:NEXT
1160 FOR J=1 TO N: FOR K=1 TO N: M(0,J,K)=0:M(N+1,J,K)=0
1170 NEXT:NEXT
1180 FOR I=1 TO N: FOR K=1 TO N: M(I,0,K)=0:M(I,N+1,K)=0
1190 NEXT:NEXT
1200 REM M=-99 MEANS NOTHING IS DRAWN
(THESE VALUES DO NOT ENTER CALCULN.)
1210 FOR I=0 TO N+1: M(0,0,I)=-99:
M(0,N+1,I)=-99: M(N+1,0,I)=-99
1220 M(N+1,N+1,I)=-99: NEXT I
1230 GOSUB 2490: REM INITIAL ENERGY
1240 GOSUB 2680: REM INITIAL MAGNETISATION
1250 NU=(NT+MA)/2
1260 IF JJ=0 THEN GOSUB 2780: REM INITIAL ENTROPY
1270 IF L$="Y" THEN GOSUB 3460: REM DRAW PICTURES
1280 REM --------------------------------------1290 REM
1300 REM
SELECT A RANDOM POINT
1310 REM
1320 REM --------------------------------------1330 N1=N1+1
1340 IP=INT(N*RND(1)+1):JP=INT(N*RND(1)+1):KP=INT(N*RND(1)+1)
1350 MO=M(IP,JP,KP):M(IP,JP,KP)=-MO
1360 GOSUB 2900: REM CALCULATE DE
1370 DM=M(IP,JP,KP)-MO
1380 REM --------------------------------------1390 REM
1400 REM
SELECT FROM PROB. DISTRIBUTION
1410 REM
1420 REM ---------------------------------------
APÉNDICE E. PROGRAMA: MODELO DE ISING EN TRES DIMENSIONES 132
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THEN
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WALK
1760
THEN
1770
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1790
IF DE<= 0 THEN 1500
IF EXP(-BETA*DE) > RND(1) THEN 1500
DM=0
DE=0
CS=0
M(IP,JP,KP)=MO
GOTO 1640
IF I$="ISOL" THEN 1620
REM ------------------------------------REM
REM
UPDATE CYCLIC BOUNDARY
REM
REM ------------------------------------IF IP=1 THEN M(N+1,JP,KP)=M(IP,JP,KP)
IF IP=N THEN M(0,JP,KP)=M(IP,JP,KP)
IF JP=1 THEN M(IP,N+1,KP)=M(IP,JP,KP)
IF JP=N THEN M(IP, 0 ,KP)=M(IP,JP,KP)
IF KP=1 THEN M(IP,JP,N+1)=M(IP,JP,KP)
IF KP=N THEN M(IP,JP, 0 )=M(IP,JP,KP)
E=E+DE: MA=MA+DM
IF L$="Y" THEN GOSUB 3660: REM UPDATE PICTURE
IF JJ <> 0 THEN 1680
DN=DM/2
IF DN<>0 THEN GOSUB 3010
S=S+CS: NU=NU+DN
REM ---------------------REM
PRINT COUNTER = NEQ
REM ---------------------IF N1=NEQ
PRINT "
- EQUILIBRIUM ASSUMED IF L$="Y" THEN LOCATE 1,1 ELSE LOCATE ,1
PRINT N1;
IF NA=NP THEN 1740
NA=NA+1:GOTO 1280
NA=1
IF L$<>"Y" THEN PRINT"
NO.";N1;"
E=";E;"
MAGNETISATION=";MA
IF L$<>"Y" THEN IF JJ=0
PRINT"
S=";S
IF N1<NEQ THEN 1280
NN=NN+1:REM INCRE. SAMPLE COUNT
REM ***********************
"
APÉNDICE E. PROGRAMA: MODELO DE ISING EN TRES DIMENSIONES 133
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REM
REM
TAKE SAMPLE
REM
REM ***********************
SE=SE+E: S2=S2+E*E: S8=S8+E^4
SM=SM+MA:S3=S3+MA*MA:S9=S9+MA^4
SS=SS+S:S4=S4+S*S
QE(NN)=E: QM(NN)=MA: REM STORED FOR CALCULATING CORRELATIONS
IF NN<SN THEN GOTO 1280
REM --------------------------------REM
REM
STATISTICAL REPORT
REM
REM --------------------------------E=SE/NN:VE=(S2/NN-E*E)*(NN/(NN-1))
EB=S2/NN:REM E SQ BAR
MA=SM/NN:VM=(S3/NN-MA*MA)*(NN/(NN-1))
S=SS/NN
VS=(S4/NN-S*S)*(NN/(NN-1))
EE=SQR(VE/NN):EM=SQR(VM/NN)
GOSUB 3130: REM CALCULATE CORRELATION COEFFICIENTS.
IF JJ=0 THEN ES=SQR(VS/NN)
IF JJ<>0 THEN GOTO 2200
MA=MA/NT:EM=EM/NT: CM=CM/NT
S=S/NT:ES=ES/NT
IF P$="N" THEN 2130
LPRINT"H= ";H,"J= ";JJ,"BETA= ";BETA:LPRINT
LPRINT"ENERGY
STD. ERROR"
LPRINT E,EE
LPRINT "MAGN.
STD ERROR"
LPRINT MA,EM
LPRINT "ENTROPY
STD ERROR"
LPRINT S,ES
LOCATE 10,8:PRINT"H= ";H,"J= ";JJ,"BETA= ";BETA:PRINT
PRINT USING "Energy=+###.##";E;
PRINT USING" Std Error=+##.##";EE
PRINT USING "
With correlns(=+##.##)";CE:PRINT
PRINT USING "Magnet=+#.###";MA;
PRINT USING" Std Error=+#.###";EM
PRINT USING "
With correlns(=+#.###)";CM:PRINT
PRINT USING "Entropy=+#.###";S;
PRINT USING" Std Error=+#.###";ES:PRINT
APÉNDICE E. PROGRAMA: MODELO DE ISING EN TRES DIMENSIONES 134
2190 GOTO 2420
2200 SV=SQR((S8/NN-EB*EB*(1-2/(NN-1)))/NN)
2210 MA=MA/NT:EM=EM/NT: CM=CM/NT:VM=VM/NT: WM=WM/NT
2220 MS=SQR(S3/NN)/NT
2230 IF P$="N" THEN 2360
2240 LPRINT "J=";JJ,"H= ";H:LPRINT
2250 LPRINT "BETA= ";BETA,"NEQ= ";NEQ:LPRINT
2260 LPRINT "ENERGY
STD. ERROR"
2270 LPRINT E,EE
2280 LPRINT "VAR(E)
VAR(VAR)"
2290 LPRINT VE,SV
2300 LPRINT "MAGNETISN. STD ERROR"
2310 LPRINT MA,EM
2320 LPRINT " R.M.S. MAGNETISATION"
2330 LPRINT MS
2340 LPRINT
2350 LPRINT:LPRINT:LPRINT:LPRINT:LPRINT
2360 PRINT USING "H=+#.#
J=+#.#
Beta=##.##";
H,JJ,BETA:PRINT
2370 PRINT USING "Energy=+###.## error ##.## (##.##)";
E,EE,CE:PRINT
2380 PRINT USING "Magnet=+#.###
error #.### (#.###)";
MA,EM,CM:PRINT
2390 PRINT USING "Var(E)=#####.# (#####.#)";VE,WE:PRINT
2400 PRINT USING "Var(M)=#.### (#.###)";VM,WM:PRINT
2410 PRINT USING "RMS Mag=#.###
Var(Var(E))=#####.#";
MS,SV:PRINT
2420 BEEP:INPUT"DO YOU WANT TO CONTINUE? (Y/N)";Y$
2430 IF Y$="N" THEN 2480
2440 INPUT"DO YOU WANT TO CHANGE ONLY BETA? (Y/N)";Y$:PRINT
2450 IF Y$="Y" THEN 560
2460 T$="NEW"
2470 GOTO 360
2480 PRINT:PRINT:PRINT"EXECUTION TERMINATED !":PRINT:PRINT:STOP
2490 REM ---------------------------------------2500 REM
2510 REM
SUBROUTINE
2520 REM
2530 REM CALCULATE INITIAL ENERGY OF SYSTEM
2540 REM
2550 REM ---------------------------------------2560 E1=0:E2=0
APÉNDICE E. PROGRAMA: MODELO DE ISING EN TRES DIMENSIONES 135
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IF HH=0 THEN GOTO 2610
FOR I=1 TO N: FOR J=1 TO N: FOR K=1 TO N
E2=E2+M(I,J,K):NEXT:NEXT:NEXT
E2=E2*HH
IF JJ=0 THEN 2660
FOR I=1 TO N: FOR J=1 TO N: FOR K=1 TO N
E1=E1+M(I,J,K)*(M(I-1,J,K)+M(I,J-1,K)+M(I,J,K-1))
NEXT:NEXT:NEXT
E1=-JJ*E1
E=E1+E2
RETURN
REM ---------------------------------------REM
REM
CALCULATE INITIAL MAGNETISATION
REM
REM ---------------------------------------MA=0
FOR I=1 TO N: FOR J=1 TO N: FOR K=1 TO N
MA=MA+M(I,J,K)
NEXT: NEXT: NEXT
RETURN
REM ---------------------------------------REM
REM
SUBROUTINE
REM
REM
CALCULATE INITIAL ENTROPY
REM
REM ---------------------------------------S=0
IF NU=0 THEN 2890
FOR IS=2 TO NU:S=S-LOG(IS):NEXT
FOR IS=NT+1-NU TO NT:S=S+LOG(IS):NEXT
RETURN
REM ----------------------------------------REM
REM
SUBROUTINE
REM
CALCULATE CHANGE IN ENERGY
REM
REM ----------------------------------------DE=M(IP+1,JP,KP)+M(IP-1,JP,KP)
DE=DE+M(IP,JP+1,KP)+M(IP,JP-1,KP)
DE=DE+M(IP,JP,KP+1)+M(IP,JP,KP-1)
APÉNDICE E. PROGRAMA: MODELO DE ISING EN TRES DIMENSIONES 136
2990 DE=-2*MO*(-JJ*DE+HH)
3000 RETURN
3010 REM ---------------------------------------3020 REM
3030 REM
SUBROUTINE
3040 REM
3050 REM
CALCULATE CHANGE IN ENTROPY
3060 REM
3070 REM ----------------------------------------3080 IF DN>0 THEN 3110
3090 CS=LOG(NU)-LOG(NT+1-NU)
3100 GOTO 3120
3110 CS=LOG(NT-NU)-LOG(NU+1)
3120 RETURN
3130 REM --------------------------------------------3140 REM
3150 REM
CALCULATE CORRELATION COEFFICIENTS
3160 REM
3170 REM --------------------------------------------3180 CLS: CE=0: CM=0:WE=0:WM=0: REM STD. ERR/VAR ALLOWING
FOR CORRELATIONS.
3190 KE=0: KM=0: KI=NN/2
3200 PRINT:PRINT "
K
RE(K)
Z1"
3210 FOR K=1 TO KI
3220 RE(K)=0: RM(K)=0
3230 FOR I=1 TO NN-K
3240 RE(K)=RE(K)+(QE(I)-E)*(QE(I+K)-E): REM CORRELATIONS IN ENERGY
3250 RM(K)=RM(K)+(QM(I)-MA)*(QM(I+K)-MA): REM CORRELATIONS
IN MAGNETISATION
3260 NEXT I
3270 RE(K)=RE(K)*2/(NN*NN)
3280 RM(K)=RM(K)*2/(NN*NN)
3290 KK=K-1
3300 Z1=2*(NN-1)*VE*SQR((2*K+1)/NN)/(NN*NN)
3310 PRINT K,RE(K),Z1
3320 IF ABS(RE(K))<Z1 THEN 3340
3330 NEXT K
3340 IF KK>NN/4 THEN RETURN: REM CORRELATIONS TOO GREAT !
3350 IF KK=0 THEN 3400
3360 FOR K=1 TO KK
3370 KE=KE+RE(K)
3380 KM=KM+RM(K)
APÉNDICE E. PROGRAMA: MODELO DE ISING EN TRES DIMENSIONES 137
3390 NEXT K
3400 WE=((NN-1)*VE+NN*NN*KE)/(NN-2*KK-1)
3410 CE=SQR(WE/NN)
3420 WM=((NN-1)*VM+NN*NN*KM)/(NN-2*KK-1)
3430 CM=SQR(WM/NN)
3440 RETURN
3450 END
3460 REM -------------------------------------3470 REM
3480 REM
DRAWING PICTURES ON MONITOR
3490 REM
3500 REM --------------------------------------3510 SCREEN 2: CLS: KEY OFF
3520 FOR I=0 TO 5: FOR J=0 TO 5: FOR K=0 TO 5
3530 PI=I: PJ=J: PK=K
3540 GOSUB 3570: REM DRAW INDIVIDUAL POINT
3550 NEXT: NEXT: NEXT
3560 RETURN
3570 REM
3580 REM
DRAW ARROW AT PI,PJ,PK
3590 XI=20+200*(PK MOD 3)+25*PI: X1=XI-10: X2=XI+10
3600 YI=20+90*INT((PK+1)/4)+14*PJ: Y1=YI-8: Y2=YI+8
3610 IF PI=0 THEN 3640 ELSE IF PI=N+1 THEN 3640 ELSE IF PJ=0 THEN 3640
ELSE IF PJ=N+1 THEN 3640 ELSE IF PK=0 THEN 3640 ELSE IF PK=N+1 THEN 3640
3620 LINE(X1,Y1)-(X2,Y2),0,BF :PSET(XI,YI):IF M(PI,PJ,PK)=1 THEN DRAW UA$
ELSE IF M(PI,PJ,PK)=-1 THEN DRAW DA$ ELSE IF M(PI,PJ,PK)=0
THEN CIRCLE (XI,YI),7
3630 RETURN
3640 LINE(X1,Y1)-(X2,Y2),0,BF :PSET(XI,YI):IF M(PI,PJ,PK)=1
THEN DRAW OUA$ ELSE IF M(PI,PJ,PK)=-1 THEN DRAW ODA$ ELSE
IF M(PI,PJ,PK)=0 THEN CIRCLE (XI,YI),7
3650 RETURN
3660 REM
3670 REM UPDATE PICTURE AT IP,JP,KP
3680 PI=IP: PJ=JP: PK=KP
3690 GOSUB 3570
3700 REM UPDATE BOUNDARY POINT
3710 IF I$="ISOL" THEN RETURN
3720 IF PI=1 THEN PI=N+1 ELSE IF PI=N THEN PI=0
3730 IF PI<>IP THEN GOSUB 3570
3740 PI=IP: IF PJ=1 THEN PJ=N+1 ELSE IF PJ=N THEN PJ=0
3750 IF PJ<>JP THEN GOSUB 3570
APÉNDICE E. PROGRAMA: MODELO DE ISING EN TRES DIMENSIONES 138
3760
3770
3780
3790
3800
3810
3820
3830
PJ=JP: IF PK=1 THEN PK=N+1 ELSE IF PK=N THEN PK=0
IF PK<>KP THEN GOSUB 3570
RETURN
REM Tutorial information
PRINT "
If you are unfamiliar with the purpose and methods of this"
PRINT "
program and simply wish to test its operation, or see an"
PRINT "
example of its outputs the following responses to the"
PRINT "
various prompts which follow are suggested:"