From 6a019dc4f91c3db3731193aa0351444462b44a24 Mon Sep 17 00:00:00 2001 From: Ian Jauslin Date: Mon, 1 Mar 2021 16:51:33 -0500 Subject: Update to v0.2: Added: Comparison of the energy for two different potentials that share the same scattering length and integral (new figure). Added: Lee-Huang-Yang prediction in figures. Fixed: Wrong exponent in definition of correlation function. Added: More precise comparison of the big equation prediction for the hard core potential (new figure). Changed: Miscellaneous minor fixes and clarifications. --- figs/hardcore.fig/Makefile | 21 ++++++++++++++-- figs/hardcore.fig/hardcore_compare.gnuplot | 36 +++++++++++++++++++++++++++ figs/hardcore.fig/hardcore_condensate.gnuplot | 9 ++++--- figs/hardcore.fig/hardcore_energy.gnuplot | 9 ++++--- 4 files changed, 67 insertions(+), 8 deletions(-) create mode 100644 figs/hardcore.fig/hardcore_compare.gnuplot (limited to 'figs/hardcore.fig') diff --git a/figs/hardcore.fig/Makefile b/figs/hardcore.fig/Makefile index 1cf8737..d8e1dfb 100644 --- a/figs/hardcore.fig/Makefile +++ b/figs/hardcore.fig/Makefile @@ -1,7 +1,7 @@ -PROJECTNAME=hardcore_energy hardcore_condensate +PROJECTNAME=hardcore_energy hardcore_compare hardcore_condensate SIMPLEQ=simpleq -DATS=simpleq-energy.dat simpleq_soft-energy.dat mueq_soft-energy.dat bigeq_soft-energy.dat simpleq-condensate.dat simpleq_soft-condensate.dat mueq_soft-condensate.dat bigeq_soft-condensate.dat +DATS=simpleq-energy.dat simpleq_soft-energy.dat mueq_soft-energy.dat bigeq_soft-energy.dat simpleq-compare.dat simpleq_soft-compare.dat mueq_soft-compare.dat bigeq_soft-compare.dat simpleq-condensate.dat simpleq_soft-condensate.dat mueq_soft-condensate.dat bigeq_soft-condensate.dat PDFS=$(addsuffix .pdf, $(PROJECTNAME)) TEXS=$(addsuffix .tikz.tex, $(PROJECTNAME)) @@ -21,6 +21,23 @@ mueq_soft-energy.dat: bigeq_soft-energy.dat: julia -p 8 $(SIMPLEQ)/main.jl -p "N=12;P=8;eq=bigeq;maxiter=100;maxlrho=0.15;nlrho=64;v_a=512;v_b=1.2494804800401416" -U tent -M medeq energy_rho_init_prevrho > $@ +simpleq-compare.dat: + julia -p 8 $(SIMPLEQ)/main.jl -p "N=12;P=8;J=5;rhos=1e-6,5e-6,1e-5,5e-5,1e-4,5e-4,1e-3,5e-3,1e-2,5e-2,1e-1,0.166,0.244" -M simpleq-hardcore energy_rho > $@-tmp + paste $@-tmp GBC99-energy.dat > $@ + rm $@-tmp +simpleq_soft-compare.dat: + julia $(SIMPLEQ)/main.jl -p "maxiter=100;v_a=328.77174503097945;v_b=1.2479228505627133;rhos=1e-6,5e-6,1e-5,5e-5,1e-4,5e-4,1e-3,5e-3,1e-2,5e-2,1e-1,0.166,0.244" -U tent -M simpleq energy_rho > $@-tmp + paste $@-tmp GBC99-energy.dat > $@ + rm $@-tmp +mueq_soft-compare.dat: + julia $(SIMPLEQ)/main.jl -p "maxiter=100;v_a=328.77174503097945;v_b=1.2479228505627133;rhos=1e-6,5e-6,1e-5,5e-5,1e-4,5e-4,1e-3,5e-3,1e-2,5e-2,1e-1,0.166,0.244" -U tent -M mueq energy_rho > $@-tmp + paste $@-tmp GBC99-energy.dat > $@ + rm $@-tmp +bigeq_soft-compare.dat: + julia -p 8 $(SIMPLEQ)/main.jl -p "N=12;P=8;eq=bigeq;maxiter=100;v_a=328.77174503097945;v_b=1.2479228505627133;rhos=1e-6,5e-6,1e-5,5e-5,1e-4,5e-4,1e-3,5e-3,1e-2,5e-2,1e-1,0.166,0.244" -U tent -M medeq energy_rho_init_prevrho > $@-tmp + paste $@-tmp GBC99-energy.dat > $@ + rm $@-tmp + simpleq-condensate.dat: julia -p 8 $(SIMPLEQ)/main.jl -p "N=12;P=8;J=5;maxlrho=0.15;nlrho=24" -M simpleq-hardcore condensate_fraction_rho > $@ simpleq_soft-condensate.dat: diff --git a/figs/hardcore.fig/hardcore_compare.gnuplot b/figs/hardcore.fig/hardcore_compare.gnuplot new file mode 100644 index 0000000..ef67c1e --- /dev/null +++ b/figs/hardcore.fig/hardcore_compare.gnuplot @@ -0,0 +1,36 @@ +set ylabel "energy relative error" +set xlabel "$\\rho$" + +set xtics 1e-6, 100, 1 +set xtics add ("$10^{-6}$" 0.000001, "$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0) +unset mxtics + +set xrange [1e-9:sqrt(2)] + +set ytics 1e-5, 10, 10 +set ytics add ("$10^{-5}$" 1e-5, "$10^{-4}$" 1e-4, "$10^{-3}$" 1e-3, "$10^{-2}$" 1e-2, "$10^{-1}$" 1e-1, "$10^{0}$" 1, "$10^1$" 10) +#unset mytics + +# default output canvas size: 12.5cm x 8.75cm +set term lua tikz size 8,6 standalone + +set key top left box linetype rgbcolor"#999999" width 0.3 height 0.3 spacing 1.3 + +# set linestyle +set style line 1 linetype rgbcolor "#4169E1" linewidth 2 dashtype "." +set style line 2 linetype rgbcolor "#DC143C" linewidth 2 +set style line 3 linetype rgbcolor "#32CD32" linewidth 2 dashtype "-" +set style line 4 linetype rgbcolor "#4B0082" linewidth 2 +set style line 5 linetype rgbcolor "#DAA520" linewidth 2 +set style line 6 linetype rgbcolor "#999999" linewidth 2 + +set pointsize 1 + +set logscale xy + +plot \ + "simpleq-compare.dat" using 1:($3<1e-2 ? 2*abs($5/2-$2)/$5 : 1/0) with lp ls 4 title "simple hc",\ + "simpleq_soft-compare.dat" using 1:($3<1e-2 ? 2*abs($5/2-$2)/$5 : 1/0) with lp ls 1 title "simple",\ + "mueq_soft-compare.dat" using 1:($3<1e-2 ? 2*abs($5/2-$2)/$5 : 1/0) with lp ls 3 title "med",\ + "bigeq_soft-compare.dat" using 1:($3<1e-2 ? 2*abs($5/2-$2)/$5 : 1/0) with lp ls 5 title "big" + diff --git a/figs/hardcore.fig/hardcore_condensate.gnuplot b/figs/hardcore.fig/hardcore_condensate.gnuplot index 974c9fd..7cd2fd2 100644 --- a/figs/hardcore.fig/hardcore_condensate.gnuplot +++ b/figs/hardcore.fig/hardcore_condensate.gnuplot @@ -24,16 +24,19 @@ set style line 2 linetype rgbcolor "#DC143C" linewidth 2 set style line 3 linetype rgbcolor "#32CD32" linewidth 2 dashtype "-" set style line 4 linetype rgbcolor "#4B0082" linewidth 2 set style line 5 linetype rgbcolor "#DAA520" linewidth 2 -set style line 6 linetype rgbcolor "#999999" linewidth 2 +set style line 6 linetype rgbcolor "#999999" linewidth 1.5 dashtype (1,5) set pointsize 1 set logscale x +a=1. + plot \ - "simpleq-condensate.dat" using 1:($3<1e-2 ? $2 : 1/0) ls 6 title "simple hc",\ + "simpleq-condensate.dat" using 1:($3<1e-2 ? $2 : 1/0) ls 4 title "simple hc",\ "simpleq_soft-condensate.dat" using 1:($3<1e-2 ? $2 : 1/0) with lines ls 1 title "simple" ,\ "mueq_soft-condensate.dat" using 1:($3<1e-2 ? $2 : 1/0) with lines ls 3 title "med",\ "bigeq_soft-condensate.dat" using 1:($3<1e-2 ? $2 : 1/0) with lines ls 5 title "big",\ - "GBC99-condensate.dat" using 1:(1-$2) ls 2 title "QMC [15]" + "GBC99-condensate.dat" using 1:(1-$2) ls 2 title "QMC [15]" ,\ + 8./(3*sqrt(pi))*sqrt(x*a**3) ls 6 title "Bog" diff --git a/figs/hardcore.fig/hardcore_energy.gnuplot b/figs/hardcore.fig/hardcore_energy.gnuplot index 9967232..d478518 100644 --- a/figs/hardcore.fig/hardcore_energy.gnuplot +++ b/figs/hardcore.fig/hardcore_energy.gnuplot @@ -23,16 +23,19 @@ set style line 2 linetype rgbcolor "#DC143C" linewidth 2 set style line 3 linetype rgbcolor "#32CD32" linewidth 2 dashtype "-" set style line 4 linetype rgbcolor "#4B0082" linewidth 2 set style line 5 linetype rgbcolor "#DAA520" linewidth 2 -set style line 6 linetype rgbcolor "#999999" linewidth 2 +set style line 6 linetype rgbcolor "#999999" linewidth 1.5 dashtype (1,5) set pointsize 1 set logscale xy +a=1. + plot \ - "simpleq-energy.dat" using 1:($3<1e-2 ? $2/$1 : 1/0) ls 6 title "simple hc",\ + "simpleq-energy.dat" using 1:($3<1e-2 ? $2/$1 : 1/0) ls 4 title "simple hc",\ "simpleq_soft-energy.dat" using 1:($3<1e-2 ? $2/$1 : 1/0) with lines ls 1 title "simple",\ "mueq_soft-energy.dat" using 1:($3<1e-2 ? $2/$1 : 1/0) every ::::95 with lines ls 3 title "med",\ "bigeq_soft-energy.dat" using 1:($3<1e-2 ? $2/$1 : 1/0) with lines ls 5 title "big",\ - "GBC99-energy.dat" using 1:($2/(2*$1)) ls 2 title "QMC [15]" + "GBC99-energy.dat" using 1:($2/(2*$1)) ls 2 title "QMC [15]" ,\ + 2*pi*a*(1+128./(15*sqrt(pi))*sqrt(x*a**3)) ls 6 title "LHY" -- cgit v1.2.3-70-g09d2