# gnuplot-dat-file index 0,1 see triang.gpl # # s=1/2 Heisenberg model for the triangular lattice # finite size + periodic boundary conditions (PBC) # see also # http://deposit.ddb.de/cgi-bin/dokserv?idn=967430151 # http://diglib.uni-magdeburg.de/Dissertationen/2003/joeschulenburg.htm # http://www-e.uni-magdeburg.de/jschulen/diss/diss.pdf # # cd spinpack/exe # gcc -o m_tilings -lm ../models/m_tilings.c # ./m_tilings 0 1 5 0 18 > daten.def # N=18 # ./m_tilings 0 6 0 0 6 > daten.def # N=36 # # idealwert nicht erreicht, wenn kx,ky=Pi nicht moeglich (N=20) # deshalb sinusfoermige FS-Scaling? use twisted boundary conditions? # SWT1+2 see Deutscher92(diss) Magnetisierung weicht stark ab (Naehe P"U) # vielleicht Abweichung SWT(N) von fit mit ED vergleichbar? # bad fit: \cite{} # # Was ist mit Magnetisierung? sort by odd/even! # # Number_of_QDJS=min(2S+1,N/2-S+1) see Bernu94 PRB50_10048 (N=36)=Ok! # check N<36! # # # GS S=1/2 allways 3ZiZj=SiSj ??? (N=27,39 yes) # 3Ediag=E ??? GAP max-QDJS-S=1 - S=0 bis min-QDJS-S=1 - S=0 ??? # # Oberflaeche? # # get the highest value lattice, try compare sz=(N-4)/2 # bad: non-bipartit, l>(1 1), l>(2 0), l!=(1,N/2) # XXZ # edgvectors Reihenfolge der Energien entspricht gut Ig even # pic2: b1=(1,0) b2=(-0.5,0.866) # Q0=(0,0), Q1=(1/3,1/3)*b # ---- QDJS --- Knick bei S=N/6 # G1: Q=Q0, Inv_am_C6_zemtrum=0 C6v^2=0 (C6v=0) # G2: Q=Q0, Inv_am_C6_zemtrum=1 C6v^2=0 (C6v=3) # G3: Q=\pm Q1=\pm(4pi/3,0) # # A=S_A, B=S_B, C=S_C # SS = 0 = AA+BB+CC + AB+AC+BC # m^2(Q) = AA+BB+CC -.5*(AB+AC+BC) = 3/2(AA+BB+CC)-SS = 3/4SMag # SMag = AA+BB+CC -1*(AB+AC+BC) = 2(AA+BB+CC)-SS # # i0 even # N L E0 E1 SMag m^2(Q) # SMag=sum/NN # 6 2 1 0 3 -4.50000000 -3.50000000 0.32500000 # ll= 3, 9 Ig=1 # min_ll=l^2=3,9 # 12 2 4 0 6 -7.32396163 -6.46078483 0.22150643 0.166130 # ll=12,12,12 Ig=2 q000 q003, e0=Q0;e1=Q1,Q0,e2=Q0,Q1,Q1,e3=Q1,Q0 n1=462/924 SL= 0 1 2 0 0 1 1 2 2 0 1 2 12 1 5 0 12 -7.25926447 -6.42670198 0.22726213 0.170446 # ll= 9,12,21 Ig=2 q_all # 18 1 5 0 18 -10.59461833 -9.90246531 0.16472007 0.12354 # ll=12,21,27 sym= 2N k=-2,0,1,- e0=Q0,e1=Q0,Q1,e2=Q1,Q0,Q1,full # 2,4,0,9=1,5,0,18=2,7,0,9=1,8,0,18 18 3 0 0 6 -10.45993564 -9.89466095 0.18211357 0.136585 # ll= 9,27,36 sym= 4N k=-11,0,- k=-11,0,+ Ig=8 q00 q00 #18 3 0 0 6 -10.45993564 -9.8894981 0.18211357 0.136585 # ... E1_2 QDJS # Ising: -4.50000000 -4.50000000 same!!! ^^^^^^^^ erstaunlich! (same korrelations! other order) # 24 2 4 0 12 -14.05459297 -13.39042030 0.12549621 0.094122 # ll=12,36,54 e=6,0,2,4 24 1 11 0 24 -14.05341276 -13.39003604 0.12557634 0.094182 # ll= 9,12 E0(Z=0,k=-4,0/24) E0(Z=1)=E0(Z=1,k=-4,8/24,-7,0/8)=lowest1=JUMP 48sym 24 1 8 0 24 -13.81148367 -13.34858090 0.14835465 0.111266 # ll= 9,49 E1(Z=1,k=-3,0/24) = 8 2 0 3 0,12,8 tested 24 1 5 0 24 -13.61120214 -13.15929802 0.15759474 0.118196 # ll=21,21,36 sym= 2N E0(Z=1)= # e=1,5,0,24: s=12..0 q000 q8 ... q000 q011 q8 q011 (kx,Inv,??) QDJS=q8,q000,q011 # 30 2 4 0 15 -17.54675277 -16.88751882 0.10045142 # ll=12 sym= 2N -16.78439671 # 010- 5+ 000+ 5.37506269 S=1-Mag 0.07968669 60sym k=-1,k/15 vt=8h e=1,8,0,30=1,14,0,30 30 1 11 0 30 -17.18630588 -16.79556770 0.12580554 # ll= 9 sym= 4N 5.41954971 # k=-6,k/30 k=015- k=000+ wf:i55=67m 30 5 1 0 6 -16.90133646 -16.51339920 0.13731789 # ll=21,36,39 sym= 2N k=00_1-, k=-9,10/30,+1 e=1,5,0,30 #30 2 7 0 15 -16.90133626 -16.51339918 # ll=21,36,39 sym= 2N -16.49811759 -16.04660784 # 60sym -2,k/15 k=0- k=5+ k=000+=0+ k=5- wf: i60=141m S=1-Mag 0.08688999 # mit LSWT bestes N=33 finden? or ud=27,6 # # N l1 l2 E0(S=0) E0(S=1) SMag 36 6 0 0 6 -20.1734422 -19.82923096 0.12480193 # ll=36,36,36 p6m s12N 2.17750458 k=000+ SMAg-wf=70h # E(k=00-,I=1)=-19.8037548 E(k=2224-)=-19.82923096 sp=i65=64h 36 1 5 0 36 -20.20989915 # ll=21,48,57 p2 s2N 2.16892423 alpha500=108h/65It e=1,8,0,36 36 6 3 0 6 -20.21640993 -19.86611477 0.12110900 # ll=27,36,63 pmm s4N 2.16978521 k0=0+ k1=44- E(k001-)=-19.84808916 wf60=45h vo=160h h_nz=18e8*5 hrmax=47 e=3,6,0,12 minE1sym= (d=0,2,4,gr=0,b60=0,ud+,144sym) (d=1,3,5,gr=4/12,b60=4/12,ud-,72sym) gr=glide-reflection(l=12) gr^2=b2-b1=(-120grd) ch190=2*64h 570M/9G (XY=-14.79853409) 36 2 7 0 18 -20.22780791 # ll=27,39,48 p2 s2N 2.16879394 thor=147h/65It e=2,13,0,18=1,11,0,36=1,18,0,36 36 3 3 0 12 -20.57699836 -20.23118621 0.10894301 # ll=9,108,117 pmm s4N 2.11397647 k0=-1,000+ voigt=i55=157h e=3,0,0,12 36 2 4 0 18 -21.05006640 -20.39034420 0.08362726 # ll=12,84,84 pmm s4N 1.92601571 k0=-1,000+ voigt1.7.4=i55=160h e=2,10,0,18 sym=-6,36k,2k,2k (v1.8.2) q12xxx0-=197h/i80=-20.39034420 q011-=-20.27598460=i75/102h ch-v1.8.3-i50=71h th-1.8.2-i80=107h # e=2,4,0,18: s=18..0 sym=-6,... q000 q12xxx0 q000 q12xxx0 q000 q12xxx0 ... # z4 q0=9.65731695 q12x0=9.69353265 q12x0=9.78783125 - q2=9.80714352 q0=9.95415325 q1=10.36362630 # z5 q12=5.70919957 q011=5.7962 q000=5.798 q8=5.848 q2=5.892 q12=5.9424 q0=6.38 # z6 q0=1.92601570 q12=1.98000078 q12=2.11931918 - q2=2.204 q0=2.3096 q0=2.3099 q12=2.47 q1=2.7606 # e=3,3,0,12: s=18..0 sym=-5,... q000 q4xx2-70 q000 q4xx2-70 q000 (4N,2N) # 6006: # capriotti99PRL82_3899 (m^+)^2(N=36)=0.7394 nonreprod. def=bernu92+bernu94 m^+(TD)=0.41=cl-59% # bernu92PRL69_2590 $m_A^2=M_A^2/(N/6(N/6+1))$ # bernu94PRB50_10048 # # 00deg,120deg (pic2 0 ...) #42 2 7 0 21 # ll=36,39,94 sym=2N e6q0=6.24717557 e=1,8,0,42=6,0,2,7(?) #42 1 5 0 42 # ll=21 sym=2N e6q0=6.23640133 e=1,17,0,42=2,10,0,21 n1=3.2e9? #42 1 14 0 42 # ll= sym=4N e6q0=6.11783005 n1= 3.2e9 flt=45GB cflt= 71GB #42 2 4 0 21 # ll=12 sym=2N e6q0=6.02128239 e=1,11,0,42 n1= 6.4e9 flt=90GB cflt=141GB # #48 4 2 0 12 # ll=12 #48 4 0 0 12 # ll=16,16,16 ? # # homogene triangles: n^2+3*m^2=ll = (0,1,4,9,16,25,...)+(0,3,12,27,...) # = 0,1,3,4,7,9,12,13,16,19,21,25,27,28,... # OR 1/4*((2n+1))^2+3/4*((2m+1))^2=ll = (1,9,25,49,...)/4+(3,27,75,...)/4 # = 1,3,7,13,19,21,... => ll*3=N_odd # i1 odd 9 3 0 0 3 -5.25000000 -3.75000000 0.26851852 0.20370370 # ll= 9, 9, 9 sym=LM Ig=0 all q11 q00 # 15 1 5 0 15 -8.55224876 -7.59683552 0.20335398 0.15334882 # ll= 9,21,21 Ig=2 # 21 1 8 0 21 -11.93666740 -11.19508007 0.16353543 0.12307675 # ll= 9 sym=4N k=-3,7,-7,0 k=-3,0,, k3/2=000 84sym new: q=-4,7/12 21 1 5 0 21 -11.78091050 -11.07846947 0.17115273 # ll=21 sym=6N q7 q0 k0=00x=-9,7/21,-2,2/3 63/126sym k1=000 # #27 1 14 0 27 -18.12547295 # nnn=same 27 3 0 0 9 -15.33483159 -14.70288550 0.13707388 # ll= 9,63,81 k=-3,1/3,-6,3/9 q00 e=3,3,0,9 27 3 6 0 9 -15.12597240 -14.52984075 0.14528581 # ll=27,27,27 sym=12N k0=-21,3/9,6/18=54/324sym 27 1 5 0 27 -15.10708651 -14.49866569 0.14658655 # ll=21,27,29 sym= 2N k0=-1,9 # q00z0=-14.48974964 #k1=00z1 : ml: i65=167h 21% E1=q00=i110=243m e=1,8,0,27=1,11,0,27 # #N l1 l2 E(S=0) E(S=1) SMag 33 1 5 0 33 -18.41177006 -17.90043336 0.13075779 # ll=21,27 s2N 0.21815105 k=-1,11=33sym z0ram=735MB= wf i70=29h+50h, z1ram=205MB voigt i50=60h ZMag= 0.04358592 XYMag= 0.08717187 SMag= 0.13075779 e=1,8,0,33=1,14,0,33 33 1 11 0 33 -18.74119735 -18.20512060 0.11791687 # ll= 9,93,111 s4N E1==k0??? ch:i65=57h k=-3,11,-8,0,-1000 n1=18e6 hnz=919e6*5 ZMag= 0.03930561 XYMag= 0.07861126 SMag= 0.11791687 diag= -6.24706686 E1= -18.74119821 wf=i60=26h/70h #33 1 17 0 33 -1.18785607 # sym=2N edges to narrow! # XY 1 7 0 33 -26.72761344 -26.52368865 FM # 1 5 0 33 SiSj=3ZiZj !!! e_diag=e/3 diag= -6.13726839 80h E1= -18.41177000 flt # i-j 0 0 SiSj 0.750000 ZiZj 0.250000 A # i-j 0 1 SiSj -0.183383 ZiZj -0.061128 B # i-j 0 2 SiSj -0.071387 ZiZj -0.023796 C # i-j 0 3 SiSj 0.165065 ZiZj 0.055022 A # i-j 0 4 SiSj -0.190236 ZiZj -0.063412 B # i-j 0 5 SiSj -0.184314 ZiZj -0.061438 C # i-j 0 6 SiSj 0.162584 ZiZj 0.054195 A # i-j 0 7 SiSj -0.082604 ZiZj -0.027535 B # i-j 0 8 SiSj -0.052783 ZiZj -0.017594 C # i-j 0 9 SiSj 0.155096 ZiZj 0.051699 A # i-j 0 10 SiSj -0.059443 ZiZj -0.019814 B # i-j 0 11 SiSj -0.064449 ZiZj -0.021483 C # i-j 0 12 SiSj 0.113724 ZiZj 0.037908 A # i-j 0 13 SiSj -0.068934 ZiZj -0.022978 B # i-j 0 14 SiSj -0.063004 ZiZj -0.021001 C # i-j 0 15 SiSj 0.112965 ZiZj 0.037655 A # i-j 0 16 SiSj -0.052534 ZiZj -0.017511 B #39 3 x 0 13 # nonABC #39 1 14 0 39 # ll= sym=4N e-6=4.09242869 e=1,14,-2,11 n1q0=ca.193e6 #39 1 5 0 39 # ll=21, sym=2N e-6=4.18236837 e=1,8,0,39=1,11,0,39 39 5 7 -2 5 -21.7060606 -21.25207676 0.11981111 # ll=39,39,39 sym=6N e-6=4.19119155 e=1,17,0,39=1,17,-2,5=3,12,-2,5=5,7,-2,5(!) n1(q0)=290e6 n1(b120)=1.8e9 # i2 best even #N l1 l2 e0 e1 SMag M^2 #12 1 5 0 12 -7.25926447 -6.42670198 0.22726213 Ig=2 better? #18 3 0 0 6 -10.45993564 -9.89466095 0.18211357 24 1 5 0 24 -13.61120214 -13.15929802 0.15759474 0.118196 30 5 1 0 6 -16.90133646 -16.51339920 0.13731789 36 6 0 0 6 -20.1734422 -19.82923096 0.12480193 0.093602 # ll=36,36,36 # i3 best odd #N l1 l2 e0.5 e1.5 SMag # 9 3 0 0 3 -5.25000000 -3.75000000 0.26851852 #15 1 5 0 15 -8.55224876 -7.59683552 0.20335400 # Ig=2 #21 1 5 0 21 -11.78091050 -11.07846947 0.17115273 # ll=9 ??? #27 3 6 0 9 -15.12597240 -14.52984075 0.14528581 27 1 5 0 27 -15.10708651 -14.49866569 0.14658655 33 1 5 0 33 -18.41177006 -17.90043336 0.13075779 39 5 7 -2 5 -21.7060606 -21.25207676 0.11981111 # ll=39,39,39 # i4 even 1th lowest SMag should scale to 0 (1D!) #12 2 4 0 6 -7.32396163 -6.46078483 0.22150643 # ll=12,12 #12 1 5 0 12 -7.25926447 -6.42670198 0.22726213 # ll=9,12 18 1 5 0 18 -10.59461833 -9.90246531 0.16472007 # ll=12 24 2 4 0 12 -14.05459297 -13.39042030 0.12549621 # ll=12,12 24 1 11 0 24 -14.05341276 -13.39003604 0.12557634 # ll=9,12 30 2 4 0 15 -17.54675277 -16.88751882 0.10045142 # ll=12 36 2 4 0 18 -21.05006640 -20.39034420 0.08362726 # ll=12 # i5 even 2nd lowest and odd 1st lowest SMag should scale to 0 ll=9 (not ll=12) #12 1 5 0 12 -7.25926447 -6.42670198 0.22726213 # ll=9,12 18 3 0 0 6 -10.45993564 -9.89466095 0.18211357 # ll=9 #24 1 11 0 24 -14.05341276 -13.39003604 0.12557634 # ll=9,12 24 1 8 0 24 -13.81148367 -13.34858090 0.14835465 # ll=9,49 30 1 11 0 30 -17.18630588 -16.79556770 0.12580554 # ll=9 36 3 3 0 12 -20.57699836 -20.23118621 0.10894301 # ll=9 # 9 3 0 0 3 -5.25000000 -3.75000000 0.26851852 # ll=9 15 1 5 0 15 -8.55224876 -7.59683552 0.20335400 # ll=9 21 1 8 0 21 -11.93666740 -11.19508007 0.16353543 # ll=9 27 3 0 0 9 -15.33483159 -14.70288550 0.13707388 # ll=9 33 1 11 0 33 -18.74119735 -18.20512060 0.11791687 # ll=9 # i6 nontripartit 12 1 3 0 12 -6.38459925 -5.41043006 # = 2 3 0 6 12 1 4 0 12 -6.93081236 -6.13305386 18 1 3 0 18 -9.51711095 -9.00169227 18 1 4 0 18 -10.05038597 -9.43880699 18 1 6 0 18 -10.32985505 -9.73467048 # = 1 7 9 18 # i7 p6m symmetric even 12 2 4 0 6 -7.32396163 -6.46078483 0.22150643 0.166130 # p6m ll=12,12 12N=144sy 36 6 0 0 6 -20.1734422 -19.82923096 0.12480193 0.093602 # p6m ll=36,36 12N=432sy #36 2 10 0 18 144sym 1.92601571 = 2 4 0 18 ? # i8 p6+p6m symmetric odd 9 3 0 0 3 -5.25000000 -3.75000000 0.26851852 # p6m ll= 9, 9 21 1 5 0 21 -11.78091050 -11.07846947 0.17115273 # p6 ll=21 6N=126sy 27 3 6 0 9 -15.12597240 -14.52984075 0.14528581 # p6m ll=36,81 12N=324sy 39 5 7 -2 5 -21.7060606 -21.25207676 # ToDo