-
Notifications
You must be signed in to change notification settings - Fork 0
/
rg_4x4_rlzn.F90
296 lines (249 loc) · 6.02 KB
/
rg_4x4_rlzn.F90
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
subroutine rg_4x4_rlzn( x1,x2,x3, SS, SSP )
implicit none
real, intent(inout) :: x1,x2,x3
! integer, intent(in) :: NX
real, intent(out) :: SS(4,3),SSP(4,3)
integer, parameter :: NX=4
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
real :: z(-1:1,-1:1,-1:1,-1:1)
integer :: a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,s
integer :: i1,i2,i3,i4,Nspin,Nconf, ii,jj,kk
integer :: NN,NNN,NNNN
real :: Econfig, boltzmann_wgt,w1,w2,w3,ZZZ,ZZp,mm1,mm2
integer :: iblock,spinsum
integer :: CCC(Nx,Nx,2**(Nx*Nx) ),CC(Nx*Nx,2**(Nx*Nx)),bccc(2,2)
real :: ZZZc( 2**(Nx*Nx) ) , EEc( 2**(Nx*Nx) )
real :: corr(NX,NX,NX,NX),tps
real :: S1,S2,S3, S11,S12,S13,S21,S22,S23,S31,S32,S33
w1=exp(x1)
w2=exp(x2)
w3=exp(x3)
S1=0.
S2=0.
S3=0.
S11=0.
S12=0.
S13=0.
S21=0.
S22=0.
S23=0.
S31=0.
S32=0.
S33=0.
! Input coupling coefficients are assumed to be in the
! form K = J/(kb*T) where J's come from Hamiltonian
!
! H = SUM_(ij=NN) J*S_i*S_j
!
! Critical value: K=0.4407... (analytical, Onsager)
!
Nspin=NX*NX
Nconf=2**Nspin
do i=1,Nspin
do c=1,Nconf
L=2**(i-1)
s=(-1)**INT( (c-1)/L )
cc( i, c ) = s
end do
end do
CCC = RESHAPE( CC, (/ NX,NX,Nconf /) )
ZZZ = 0.
! 2x2
!---------
! c d
! a b
!---------
do kk=1,Nconf
NN = 0.
NNN = 0.
NNNN = 0.
do j=1,NX-1
do i=1,NX-1
a = ccc(i,j,kk)
b = ccc(i+1,j,kk)
c = ccc(i,j+1,kk)
d = ccc(i+1,j+1,kk)
NN = NN + a*b + a*c
NNN = NNN + a*d + b*c
NNNN = NNNN + a*b*c*d
end do
end do
#if 1
! Periodic Boundaries
do j=1,NX-1
i=NX
a = ccc(i,j,kk)
b = ccc(1,j,kk)
c = ccc(i,j+1,kk)
d = ccc(1,j+1,kk)
NN = NN + a*c + a*b
NNN = NNN + a*d + b*c
NNNN = NNNN + a*b*c*d
end do
j=NX
do i=1,NX-1
a = ccc(i,j,kk)
b = ccc(i+1,j,kk)
c = ccc(i,1,kk)
d = ccc(i+1,1,kk)
NN = NN + a*b + a*c
NNN = NNN + a*d + b*c
NNNN = NNNN + a*b*c*d
end do
j=NX
i=NX
a = ccc(i,j,kk)
b = ccc(1,j,kk)
c = ccc(i,1,kk)
d = ccc(1,1,kk)
NN = NN + a*b + a*c
NNN = NNN + a*d + b*c
NNNN = NNNN + a*b*c*d
#endif
Econfig = x1*NN + x2*NNN + x3*NNNN
boltzmann_wgt = exp( Econfig )
! Now calculate even <spin-spin> terms for config kk
S1 = S1 + boltzmann_wgt*dble( NN )
S2 = S2 + boltzmann_wgt*dble( NNN )
S3 = S3 + boltzmann_wgt*dble( NNNN )
S11 = S11 + boltzmann_wgt*dble( NN * NN )
S21 = S21 + boltzmann_wgt*dble( NNN * NN )
S31 = S31 + boltzmann_wgt*dble( NNNN * NN )
S12 = S12 + boltzmann_wgt*dble( NN * NNN )
S22 = S22 + boltzmann_wgt*dble( NNN * NNN )
S32 = S32 + boltzmann_wgt*dble( NNNN * NNN )
S13 = S13 + boltzmann_wgt*dble( NN * NNNN )
S23 = S23 + boltzmann_wgt*dble( NNN * NNNN )
S33 = S33 + boltzmann_wgt*dble( NNNN * NNNN )
ZZZ = ZZZ + boltzmann_wgt
ZZZc(kk)=boltzmann_wgt
EEc(kk) = Econfig
end do
S1=S1/ZZZ
S2=S2/ZZZ
S3=S3/ZZZ
SS(1,1) = S11 / ZZZ - S1*S1
SS(1,2) = S12 / ZZZ - S1*S2
SS(1,3) = S13 / ZZZ - S1*S3
SS(2,1) = S21 / ZZZ - S2*S1
SS(2,2) = S22 / ZZZ - S2*S2
SS(2,3) = S23 / ZZZ - S2*S3
SS(3,1) = S31 / ZZZ - S3*S1
SS(3,2) = S32 / ZZZ - S3*S2
SS(3,3) = S33 / ZZZ - S3*S3
SS(4,1) = S1
SS(4,2) = S2
SS(4,3) = S3
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
S1=0.
S2=0.
S3=0.
S11=0.
S12=0.
S13=0.
S21=0.
S22=0.
S23=0.
S31=0.
S32=0.
S33=0.
! a b
! 4x4 ===>
! 2x2
!---------
! cc dd
! aa bb
!---------
do kk=1,Nconf
NN = 0.
NNN = 0.
NNNN = 0.
do j=1,3,2
do i=1,3,2
a = ccc(i,j,kk)
b = ccc(i+1,j,kk)
c = ccc(i,j+1,kk)
d = ccc(i+1,j+1,kk)
spinsum=a+b+c+d
if (spinsum /= 0) then
spinsum = spinsum/abs(spinsum)
else
spinsum = c
endif
ii = (i+1)/2
jj = (j+1)/2
bccc(ii,jj)=spinsum
end do
end do
do j=1,1
do i=1,1
a = bccc(i,j)
b = bccc(i+1,j)
c = bccc(i,j+1)
d = bccc(i+1,j+1)
NN = NN + a*b + a*c
NNN = NNN + a*d + b*c
NNNN = NNNN + a*b*c*d
end do
end do
#if 1
! Periodic Boundaries
j=1
i=2
a = bccc(i,j)
b = bccc(1,j)
c = bccc(i,j+1)
d = bccc(1,j+1)
NN = NN + a*c + a*b
NNN = NNN + a*d + b*c
NNNN = NNNN + a*b*c*d
j=2
i=1
a = bccc(i,j)
b = bccc(i+1,j)
c = bccc(i,1)
d = bccc(i+1,1)
NN = NN + a*b + a*c
NNN = NNN + a*d + b*c
NNNN = NNNN + a*b*c*d
j=2
i=2
a = bccc(i,j)
b = bccc(1,j)
c = bccc(i,1)
d = bccc(1,1)
NN = NN + a*b + a*c
NNN = NNN + a*d + b*c
NNNN = NNNN + a*b*c*d
#endif
! Now calculate even <spin-spin> terms for config kk
boltzmann_wgt=ZZZc(kk)
S1 = S1 + boltzmann_wgt*dble( NN )
S2 = S2 + boltzmann_wgt*dble( NNN )
S3 = S3 + boltzmann_wgt*dble( NNNN )
S11 = S11 + boltzmann_wgt*dble( NN * NN )
S21 = S21 + boltzmann_wgt*dble( NNN * NN )
S31 = S31 + boltzmann_wgt*dble( NNNN * NN )
S12 = S12 + boltzmann_wgt*dble( NN * NNN )
S22 = S22 + boltzmann_wgt*dble( NNN * NNN )
S32 = S32 + boltzmann_wgt*dble( NNNN * NNN )
S13 = S13 + boltzmann_wgt*dble( NN * NNNN )
S23 = S23 + boltzmann_wgt*dble( NNN * NNNN )
S33 = S33 + boltzmann_wgt*dble( NNNN * NNNN )
end do
S1=S1/ZZZ
S2=S2/ZZZ
S3=S3/ZZZ
SSp(1,1) = S11 / ZZZ - S1*S1
SSp(1,2) = S12 / ZZZ - S1*S2
SSp(1,3) = S13 / ZZZ - S1*S3
SSp(2,1) = S21 / ZZZ - S2*S1
SSp(2,2) = S22 / ZZZ - S2*S2
SSp(2,3) = S23 / ZZZ - S2*S3
SSp(3,1) = S31 / ZZZ - S3*S1
SSp(3,2) = S32 / ZZZ - S3*S2
SSp(3,3) = S33 / ZZZ - S3*S3
SSp(4,1) = S1
SSp(4,2) = S2
SSp(4,3) = S3
end subroutine rg_4x4_rlzn