# gnuplot-file
#
# 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
#
#set term dumb
# E     = A0      + A3*L^-3
# GAP   = D4*L^-2 + D5*L^-3
# N*GAP = D4      + D5*L^-1
# Mag   = M0      + M1*L^-1
#
ps=1
ps=0

set pointsize 1.5
d4=12.1936
a4=0.1
b4=0.1
a45=0.1
b45=0.1
# x=L^3
e0(x)=a0  + a3*x + 0*a4*x**(4/3.)
# x=L
eb(x)=a0b + a2b*x**(-8)  # + a3b*x**(-3)
a0b= -0.584265     #   +/- 5.923e-05    (0.01014%)
a2b= -452.059      #   +/- 11.27        (2.493%)
# x=L entspricht extrem gut LC f(log(x))-verlauf
ec(x)=a0c + a2c*x**(-4)  # + a3b*x**(-3)
a0c= -0.568335       # +/- 6.478e-05    (0.0114%)
a2c= -4.13173        # +/- 0.03418      (0.8272%)
ed(x)=a0d + a2d*x**(-7)  # + a3b*x**(-3)
a0d= -0.567629      #  +/- 4.998e-05    (0.008805%)
a2d= -34.306        #  +/- 0.2407       (0.7016%)
#
#
e1(x)=b0 + b3*x+ 0*b4*x**(4/3.)
e05(x)=a05 + a35*x+ 0*a45*x**(4/3.)
e15(x)=b05 + b35*x+ 0*b45*x**(4/3.)
g(x)=            d4          + d5*x
g1(x)=           d41         + d51*x
g3(x)=           g30         + g31*x
m(x)=            m0          + m1*x
mb(x)=           m0b         + m1b*x +m2b*x**2
mc(x)=           m0c         + m1c*x +0*x**2
m2(x)=           m02         + m12*x +0*x**2
 fit e0(x)  "triang.dat" i 2 u ($1**(-3/2.)):($6/$1) via a0,a3
#fit eb(x)  "triang.dat" i 4 u ($1**(1/2.)):($6/$1) via a0b,a2b
 fit ec(x)  "-" u ($1**(1/2.)):($6/$1) via a0c,a2c
#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          
e
 fit ed(x)  "-" u ($1**(1/2.)):($6/$1) via a0d,a2d
  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
e
#fit e1(x)  "triang.dat" i 2 u ($1**(-3/2.)):($7/$1) via b0,b3
 fit e05(x) "triang.dat" i 3 u ($1**(-3/2.)):($6/$1) via a05,a35
#fit e15(x) "triang.dat" i 3 u ($1**(-3/2.)):($7/$1) via b05,b35
#fit e0(x)  "triang.dat" i 2 u ($1**(-3/2.)):($6/$1):($6/$1-e0(1/$1**(3/2.))) via a0,a3,a4
#fit e1(x)  "triang.dat" i 2 u ($1**(-3/2.)):($7/$1):($7/$1-e1(1/$1**(3/2.))) via b0,b3,b4
 fit [0.17:] g(x) "triang.dat" i 2 u ($1**(-1/2.)):(($7-$6)*$1) via d4,d5
 fit g1(x)  "triang.dat" i 3 u ($1**(-1/2.)):(($7-$6)*$1) via d41,d51
 fit g3(x)  "triang.dat" i 2 u ($1**(-1.)):(($7-$6)) via g30,g31
 fit m(x)   "triang.dat" i 2 u ($1**(-1/2.)):(($8)**.5) via m0,m1
 fit mb(x)  "triang.dat" i 5 u ($1**(-1/2.)):(($8)**.5) via m0b,m1b,m2b
 fit mc(x)  "triang.dat" i 4 u ($1**(-1/2.)):(($8)**.5) via m0c,m1c
# (SiSj)<SiSj>
 fit m2(x)  "triang.dat" i 2 u ($1**(-1/2.)):(($9)**.5) via m02,m12
# fit taken by betts

if(ps==1)set term postscript eps enhanced mono dashed "Helvetica" 20; set out "tmp/t1_erg.eps"
set key right spacing 1.2
fx(x)=x**(-3/2.)
yy=-0.534
set label 5 "N:" at fx(56),yy center
set label 1 "15" at fx(15),yy center
set label 2 "21" at fx(21),yy center
set label 3 "27" at fx(27),yy center
set label 4 "33" at fx(33),yy center
yy=-0.615
set label 6 "N:" at fx(56),yy center
set label 7 "12" at fx(12),yy center
set label 8 "18" at fx(18),yy center
set label   "24" at fx(24),yy center
set label   "36" at fx(36),yy center
# PRB61_11529trumper00
set arrow from 0.002,-0.5388 to 0,-0.5388
set label "LSWT" at 0.0022,-0.539
# miyake92:
set arrow from 0.002,-0.5468 to 0,-0.5468
set label "SWT2" at 0.0022,-0.548
# PRB61_11529trumper00[14]
set arrow from 0.002,-0.5458 to 0,-0.5458
set label "QMC" at 0.0022,-0.544
set xlabel "L^{-3}"
set ylabel "E/N"
# Skaling odd S=1/2 down to S=0 by E(S) PRL69_2590bernu
plot [0:] [-0.62:-0.53] e0(x) t "" w l lt 1,e05(x) t "" w l lt 1,\
eb(x**(-1/3.)) t "l^2=12" w l 2 2,\
ec(x**(-1/3.)) t "l^2= 9" w l 3 3,\
ed(x**(-1/3.)) t "" w l 3 3,\
"triang.dat"\
    i 7 u ($1**(-3/2.)):($6/$1) t "" w p pt 2,\
 "" i 8 u ($1**(-3/2.)):($6/$1) t "" w p pt 2,\
 "" i 1 u ($1**(-3/2.)):($6/$1) t  "odd E_0/N" w p pt 6,\
 "" i 0 u ($1**(-3/2.)):($6/$1) t "even E_0/N" w p pt 4
#
if(ps==0)pause -1
set nolabel
set noarrow

if(ps==1)set term postscript eps enhanced mono dashed "Helvetica" 20; set out "tmp/t1_gap1.eps"
set key left
yy=0.05
set label 5 "N:" at 42**(-1.),yy center
set label 1 "9"  at  9**(-1.),yy center
set label 2 "15" at 15**(-1.),yy center
set label 3 "21" at 21**(-1.),yy center
set label 4 "27" at 27**(-1.),yy center
set xlabel "L^{-2}"
set ylabel "{/Symbol D}"
plot [0:1./8] [0.:1.] g3(x) t "",\
 "triang.dat" i 8 u (1/$1):(2./3*($7-$6)) t "" w p pt 2,\
 "" i 7 u (1/$1):($7-$6) t "" w p pt 2,\
 "" i 4 u (1/$1):($7-$6) smooth cspline t "l^2=12" w l lt 2,\
 "" i 0 u (1/$1):($7-$6) t "even {/Symbol D}" w p pt 4,\
 "" i 1 u (1/$1):(2./3*($7-$6)) t "odd {/Symbol D}2/3" w p pt 6
# "" i 6 u (1/$1):($7-$6) t "Nt even {/Symbol D}",\
#
if (ps==0) pause -1
set nolabel
set noarrow

if(ps==1)set term postscript eps enhanced mono dashed "Helvetica" 20; set out "tmp/t1_gap.eps"
set key right
yy=5.5
set label 5 "N:" at  0.05,yy center
set label 1 "9"  at  9**(-1/2.),yy center
set label 2 "15" at 15**(-1/2.),yy center
set label 3 "21" at 21**(-1/2.),yy center
set label 4 "27" at 27**(-1/2.),yy center
set xlabel "L^{-1}"
set ylabel "N{/Symbol D}"
set arrow from 0.02,16.334 to 0,16.334
set label "LSWT" at 0.01,15.6
# PRB61_11529trumper00FS-SW: 1/(2\chi)_{sw}=N*(E(S)-E0)/(S(S+1))=8.167
plot [0:0.37] [5.:22.] g(x) t "" w l lt 1, 2./3*g1(x) t "" w l lt 1,\
 "triang.dat" i 8 u (1/$1**(1/2.)):(2./3*($7-$6)*$1) t "" w p pt 2,\
 "" i 7 u (1/$1**(1/2.)):(($7-$6)*$1) t "" w p pt 2,\
 "" i 4 u (1/$1**(1/2.)):(($7-$6)*$1) smooth cspline t "l^2=12" w l lt 2,\
 "" i 0 u (1/$1**(1/2.)):(($7-$6)*$1) t "even N{/Symbol D}" w p pt 4,\
 "" i 1 u (1/$1**(1/2.)):(2./3*($7-$6)*$1) t "odd N{/Symbol D}2/3" w p pt 6
# "" i 6 u (1/$1**(1/2.)):(($7-$6)*$1) t "Nt even N{/Symbol D}",\
#
if (ps==0) pause -1
set nolabel
set noarrow

if(ps==1)set term postscript eps enhanced mono dashed "Helvetica" 20; set out "tmp/t1_gap3.eps"
set key right
yy=5.5
set label 5 "N:" at  0.05,yy center
set label 1 "9"  at  9**(-1/2.),yy center
set label 2 "15" at 15**(-1/2.),yy center
set label 3 "21" at 21**(-1/2.),yy center
set label 4 "27" at 27**(-1/2.),yy center
set xlabel "L^{-1}"
set ylabel "{E_3-E_0}"
set arrow from 0.02,16.334 to 0,16.334
set label "LSWT" at 0.01,15.6
# PRL82_3899capriotti99 D3=E3-E0 (S=3multiple for full sym of H or WF(2)(?))
# N=12, 36 exact data lineary extrapolated produce a large finite value
#plot [0:0.09] [0.:5.] \
# "-" u (1/$1):(($7-$6)) t "" w p pt 2
#
##
#if (ps==0) pause -1
set nolabel
set noarrow

if(ps==1) set term postscript eps enhanced mono dashed "Helvetica" 20; set out "tmp/t1_mag.eps"
yy=0.27
yy=0.03
set key left
set label 6 "N:" at 48**(-1/2.),yy center
set label 1 "9"  at  9**(-1/2.),yy center
set label 2 "15" at 15**(-1/2.),yy center
set label 3 "21" at 21**(-1/2.),yy center
set label 4 "27" at 27**(-1/2.),yy center
set label 5 "36" at 36**(-1/2.),yy center
set xlabel "L^{-1}"
set ylabel "m^+"
set arrow from 0.02,0.2387*(2./3)**.5 to 0,0.2387*(2./3)**.5
set label "LSWT^*" at 0.01,0.255*(2./3)**.5
plot [0*0.15:0.37] [0*0.25:0.55] m(x) t "",\
 mb(x) t "l^2= 9" w l 3 3,\
 mc(x) t "l^2=12" w l 2 2,\
 "triang.dat" i 7 u (1/$1**(1/2.)):(($8)**.5) t "" w p pt 2,\
 "" i 8 u ($1**(-1/2.)):(($8)**.5) t ""           w p pt 2,\
 "" i 1 u ($1**(-1/2.)):(($8)**.5) t "odd m^+"    w p pt 6,\
 "" i 0 u ($1**(-1/2.)):(($8)**.5) t "even m^+"   w p pt 4
# (0.2387+1.215*x-0*1.5*x*x) # SW deutscher92 weicht stark ab (da nahe PUE)
#    da anders berechnet! mit SaSa mit Faktor 2 gegenueber SaSb
# M^2 =(AA+BB+CC  -AB   -BC   -CA )/3^2 cl: (1+1+1+0.5+0.5+0.5)/9=1/2
# Ma^2=(AA+BB+CC+2|AB|+2|BC|+2|CA|)/9^2 cl: (1+1+1+1  +1  +1  )/9=3/2
if(ps==0)pause -1
set nolabel
set noarrow

if(ps==1) set term postscript eps enhanced mono dashed "Helvetica" 20; set out "tmp/t1_smag.eps"
yy=0.36
set key left
set label 6 "N:" at 42**(-1/2.),yy center
set label 1 "9"  at  9**(-1/2.),yy center
set label 2 "15" at 15**(-1/2.),yy center
set label 3 "21" at 21**(-1/2.),yy center
set label 4 "27" at 27**(-1/2.),yy center
set label 5 "36" at 36**(-1/2.),yy center
set xlabel "L^{-1}"
set ylabel "m"
c=2.0
plot [.15:.37] [.35:.65] (3./2)**.5*m(x) t "" w l lt 1, (c)**.5*m2(x) t "" w l lt 1,\
 "triang.dat"\
    i 1 u ($1**(-.5)):((3./2*$8)**.5) t "(3/2)^{1/2}m^+" w p pt 2,\
 "" i 0 u ($1**(-.5)):((3./2*$8)**.5) t ""  w p pt 2,\
 "" i 1 u ($1**(-.5)):((c*$9)**.5)    t "m" w p pt 4,\
 "" i 0 u ($1**(-.5)):((c*$9)**.5)    t ""  w p pt 4,\
 0.2387+1.215*x-0*1.5*x*x             t "LSWT" w l lt 2
# (0.2387+1.215*x-0*1.5*x*x) # LSWT deutscher92 weicht stark ab (da nahe PUE)
#    da anders berechnet! mit SaSa mit Faktor 2 gegenueber SaSb
# FS-Korrektur klassischer Natur? K-punkte aus kl. Dispersion?
if(ps==0)pause -1