many changes

4 files changed, 61 insertions, 15 deletions

diff --git a/essential-ising.bib b/essential-ising.bib
index 16a0883..f490dd9 100644
--- a/essential-ising.bib
+++ b/essential-ising.bib
@@ -115,7 +115,6 @@
   year={2013}
 }
 
-
 @article{dimitrovic.1991.finite,
   title={Finite-size effects, goldstone bosons and critical exponents in the d= 3 Heisenberg model},
   author={Dimitrovi{\'c}, I and Hasenfratz, P and Nager, J and Niedermayer, Ferenc},
diff --git a/essential-ising.tex b/essential-ising.tex
index 9397aa0..ba8e452 100644
--- a/essential-ising.tex
+++ b/essential-ising.tex
@@ -281,6 +281,7 @@ and their constants of integration fixed by known zero field values, yielding
     &=\fM(0)+\frac{AB}{\pi}\bigg(1-\frac{Y-1}Ye^{1/Y}\ei(-1/Y)\bigg)\\
   \fF^\twodee(Y/B)
     &=-Y\bigg(\frac{\fM(0)}B-\frac{A}\pi e^{1/Y}\ei(-1/Y)\bigg)
+    \label{eq:2d_free_scaling}
 \end{align}
 with $F(t,h)=|t|^{2-\alpha}\fF(h|t|^{-\beta\delta})+t^{2-\alpha}\log|t|$ in
 two dimensions.
@@ -364,12 +365,13 @@ correction appears to match data quite well.
     $h|t|^{-\beta\delta}$. Points with error bars show data with sampling
     error taken from simulations of a $4096\times4096$ square-lattice Ising
     model with periodic boundary conditions and $T_\c-T=0.01,0.02,\ldots,0.1$
-    and $H=0.1\times(1,2^{-1/4},\ldots,2^{-50/4})$. Color denotes the value of
-    $T$, with red corresponding to $0.01$ and violet to $0.1$. The solid lines
+    and $H=0.1\times(1,2^{-1/4},\ldots,2^{-50/4})$. The solid blue lines
     show our analytic results \eqref{eq:sus_scaling} and
-    \eqref{eq:mag_scaling}, while the dashed lines show fits of
-    \eqref{eq:sus_scaling_poly} and \eqref{eq:mag_scaling_poly} to the data
-    for $N=0$, with $c_0=-0.0124$ and $\lambda=1.77$.
+    \eqref{eq:mag_scaling}, the dashed yellow lines show 
+    \eqref{eq:sus_scaling_poly} and \eqref{eq:mag_scaling_poly} for $N=0$, the
+    dotted green lines show the same for $N=4$, and the red line show the
+    polynomial resulting from truncating the series after the eight known
+    terms.
   }
   \label{fig:scaling_fits}
 \end{figure}
@@ -377,7 +379,13 @@ correction appears to match data quite well.
 \begin{figure}
   \input{fig-series}
   \caption{
-    Something
+    The series coefficients defined by $\tilde\fF(X)=\sum_nf_nX^n$. The blue
+    pluses correspond to the scaling form \eqref{eq:2d_free_scaling}, the
+    yellow saltires correspond to that form with the first four coefficients
+    fixed to known values (\eqref{eq:sus_scaling_poly} with $N=0$), the green
+    stars correspond to that form with the first eight coefficients fixed to
+    known values (\eqref{eq:sus_scaling_poly} with $N=4$), and the red squares
+    correspond to the first eight coefficients.
   }
   \label{fig:series}
 \end{figure}
diff --git a/figs/fig-series.gplot b/figs/fig-series.gplot
index bde0cae..b9cfc57 100644
--- a/figs/fig-series.gplot
+++ b/figs/fig-series.gplot
@@ -1,13 +1,26 @@
 
 set terminal pslatex rotate size 3.417,2.111
 
+cc1 = "#5e81b5"
+cc2 = "#e19c24"
+cc3 = "#8fb032"
+cc4 = "#eb6235"
+
 set logscale y
 
 data = "figs/fig-series-data.dat"
 
-set xrange [0:20]
-set yrange [0.000001:10]
+set xrange [0:30]
+set yrange [0.000004:600]
 set key off
+set xlabel '$n$'
+set ylabel offset 2 '$|f_n|$'
+
+set ytics format '\footnotesize$10^{%T}$' 0.00001,10,1000
 
-plot data using 1:2 with points, data using 1:3 with points, data using 1:4 with points, data using 1:5 with points
+plot \
+  data using 1:2 with points lc rgb cc1, \
+  data using 1:3 with points lc rgb cc2, \
+  data using 1:4 with points lc rgb cc3, \
+  data using 1:5 with points lc rgb cc4
 
diff --git a/figs/fig-susmag.gplot b/figs/fig-susmag.gplot
index 80679b6..c56c898 100644
--- a/figs/fig-susmag.gplot
+++ b/figs/fig-susmag.gplot
@@ -2,6 +2,11 @@
 set terminal pslatex rotate size 3.417,4.222
 set multiplot
 
+cc1 = "#5e81b5"
+cc2 = "#e19c24"
+cc3 = "#8fb032"
+cc4 = "#eb6235"
+
 Tc = 2 / log(1 + sqrt(2))
 Delta = 15. / 8
 gamma = 7. / 4
@@ -52,7 +57,7 @@ magfunc = "figs/fig-mag_scaling-func.dat"
 
 num = "data/data_square-4096.dat"
 
-set samples 10000
+set samples 20000
 set key off
 
 set size 1,1 - 0.52
@@ -66,7 +71,12 @@ set mxtics 5
 set mytics 5
 set bmargin 0.2
 
-plot num using (X($2, $3)):(10**3 * Tc * $10 * t($2)**gamma):(10**3 * Tc * $11 * t($2)**gamma):(hsv2rgb(20 * t($2), 1, 1)) with yerrorbars pt 0 lc rgb variable, susfunc using (10**$1 / B):(10**(3+$2) * A * B**2) with linespoints pt 0 lw 2 lc rgb "black", susfunc using (10**$1 / B2):(10**(3+$2) * A2 * B2**2 + 10**3 * (sum[i=1:n] poly(c(i), lamb, i-1, 10**$1))) with lines dt 2 lw 2 lc black, susfunc using (10**$1 / B3):(10**(3+$2) * A3 * B3**2 + 10**3 * (sum[i=1:n2] poly(c2(i), lamb2, i-1, 10**$1))) with lines dt 3 lw 2 lc black, susfunc using (10**$1 / B3):(-10**3 * (sum[i=1:7] GC(i + 1) * i * (i + 1) * (10**$1 / B3)**(i-1))) with lines dt 5 lw 2 lc black
+plot \
+  num using (X($2, $3)):(10**3 * Tc * $10 * t($2)**gamma):(10**3 * Tc * $11 * t($2)**gamma) with yerrorbars pt 0 lc black, \
+  susfunc using (10**$1 / B):(10**(3+$2) * A * B**2) with linespoints pt 0 lw 2 lc rgb cc1 dt 1, \
+  susfunc using (10**$1 / B2):(10**(3+$2) * A2 * B2**2 + 10**3 * (sum[i=1:n] poly(c(i), lamb, i-1, 10**$1))) with lines lw 2 lc rgb cc2 dt 2, \
+  susfunc using (10**$1 / B3):(10**(3+$2) * A3 * B3**2 + 10**3 * (sum[i=1:n2] poly(c2(i), lamb2, i-1, 10**$1))) with lines lw 2 lc rgb cc3 dt 3, \
+  -10**3 * (sum[i=1:7] GC(i + 1) * i * (i + 1) * (x)**(i-1)) with lines lw 2 lc rgb cc4 dt 4
 
 set bmargin -1
 set tmargin 0.2
@@ -77,7 +87,12 @@ set ylabel offset 1,0 '$M|t|^{-\beta}$'
 set xlabel '$h|t|^{-\beta\delta}$'
 set xtics format '%g'
 
-plot num using (X($2, $3)):($6 * t($2)**(-beta)):($7 * t($2)**(-beta)):(hsv2rgb(20 * t($2), 1, 1)) with yerrorbars pt 0 lc rgb variable, magfunc using (10**$1 / B):(M0 + 10**($2) * A * B) with linespoints pt 0 lw 2 lc black, magfunc using (10**$1 / B2):(M0 + 10**($2) * A2 * B2 + (sum[i=1:n] polyint(c(i), lamb, i-1, 10**$1)) / B2) smooth csplines with lines dt 2 lw 2 lc black, magfunc using (10**$1 / B3):(M0 + 10**($2) * A3 * B3 + (sum[i=1:n2] polyint(c2(i), lamb2, i-1, 10**$1)) / B3) smooth csplines with lines dt 3 lw 2 lc black, magfunc using (10**$1 / B):(-sum[i=1:8] GC(i) * i * (10**$1 / B)**(i-1)) with lines dt 5 lw 2 lc black
+plot \
+  num using (X($2, $3)):($6 * t($2)**(-beta)):($7 * t($2)**(-beta)) with yerrorbars pt 0 lc black, \
+  magfunc using (10**$1 / B):(M0 + 10**($2) * A * B) with linespoints pt 0 lw 2 lc rgb cc1 dt 1, \
+  magfunc using (10**$1 / B2):(M0 + 10**($2) * A2 * B2 + (sum[i=1:n] polyint(c(i), lamb, i-1, 10**$1)) / B2) smooth csplines with lines lw 2 lc rgb cc2 dt 2, \
+  magfunc using (10**$1 / B3):(M0 + 10**($2) * A3 * B3 + (sum[i=1:n2] polyint(c2(i), lamb2, i-1, 10**$1)) / B3) smooth csplines with lines lw 2 lc rgb cc3 dt 3, \
+  -sum[i=1:8] GC(i) * i * x**(i-1) with lines lw 2 lc rgb cc4 dt 4
 
 set logscale xy
 set tmargin -1
@@ -94,7 +109,13 @@ set xtics add ('$\footnotesize10^{-2}$' 10**(-2), "" 0.1, '$\footnotesize10^0$'
 set mytics 5
 set ytics format '\footnotesize$10^{%T}$' 0.00001,10,0.01
 
-plot num using (X($2, $3)):(Tc * $10 * t($2)**gamma):(Tc * $11 * t($2)**gamma):(hsv2rgb(20 * t($2), 1, 1)) with yerrorbars pt 0 lc rgb variable, susfunc using (10**$1 / B):(10**$2 * A * B**2) with linespoints pt 0 lw 2 lc rgb "black", susfunc using (10**$1 / B2):(10**$2 * A2 * B2**2 + (sum[i=1:n] poly(c(i), lamb, i-1, 10**$1))) with lines dt 2 lw 2 lc black, susfunc using (10**$1 / B3):(10**$2 * A3 * B3**2 + (sum[i=1:n2] poly(c2(i), lamb2, i-1, 10**$1))) with lines dt 3 lw 2 lc black, susfunc using (10**$1 / B):(-sum[i=2:8] GC(i) * i * (i-1) * (10**$1 / B)**(i-2)) with lines dt 5 lw 2 lc black
+plot \
+  num using (X($2, $3)):(Tc * $10 * t($2)**gamma):(Tc * $11 * t($2)**gamma) with yerrorbars pt 0 lc black, \
+  susfunc using (10**$1 / B):(10**$2 * A * B**2) with linespoints pt 0 lw 2 lc rgb cc1 dt 1, \
+  susfunc using (10**$1 / B2):(10**$2 * A2 * B2**2 + (sum[i=1:n] poly(c(i), lamb, i-1, 10**$1))) with lines lw 2 lc rgb cc2 dt 2, \
+  susfunc using (10**$1 / B3):(10**$2 * A3 * B3**2 + (sum[i=1:n2] poly(c2(i), lamb2, i-1, 10**$1))) with lines lw 2 lc rgb cc3 dt 3, \
+  -sum[i=2:8] GC(i) * i * (i-1) * x**(i-2) with lines dt 4 lw 2 lc rgb cc4, \
+  0.0705991 * x**(-14./15)
 
 unset logscale xy
 set logscale x
@@ -105,5 +126,10 @@ set ylabel offset 4,0 '\footnotesize$M|t|^{-\beta}$'
 set ytics format '\footnotesize {%g}' 1.2,0.2,1.8
 set mytics 5
 
-plot num using (X($2, $3)):($6 * t($2)**(-beta)):($7 * t($2)**(-beta)):(hsv2rgb(20 * t($2), 1, 1)) with yerrorbars pt 0 lc rgb variable, magfunc using (10**$1 / B):(M0 + A * B * 10**$2) with linespoints pt 0 lw 2 lc black, magfunc using (10**$1 / B2):(M0 + 10**($2) * A2 * B2 + (sum[i=1:n] polyint(c(i), lamb, i-1, 10**$1)) / B2) with lines dt 2 lw 2 lc black, magfunc using (10**$1 / B3):(M0 + 10**($2) * A3 * B3 + (sum[i=1:n2] polyint(c2(i), lamb2, i-1, 10**$1)) / B3) with lines dt 3 lw 2 lc black, magfunc using (10**$1 / B):(-sum[i=1:8] GC(i) * i * (10 **$1 / B)**(i-1)) with lines dt 5 lw 2 lc black
+plot \
+  num using (X($2, $3)):($6 * t($2)**(-beta)):($7 * t($2)**(-beta)) with yerrorbars pt 0 lc black, \
+  magfunc using (10**$1 / B):(M0 + A * B * 10**$2) with linespoints pt 0 lw 2 lc rgb cc1 dt 1, \
+  magfunc using (10**$1 / B2):(M0 + 10**($2) * A2 * B2 + (sum[i=1:n] polyint(c(i), lamb, i-1, 10**$1)) / B2) with lines lw 2 lc rgb cc2 dt 2, \
+  magfunc using (10**$1 / B3):(M0 + 10**($2) * A3 * B3 + (sum[i=1:n2] polyint(c2(i), lamb2, i-1, 10**$1)) / B3) with lines lw 2 lc rgb cc3 dt 3, \
+  -sum[i=1:8] GC(i) * i * x**(i-1) with lines lw 2 lc rgb cc4 dt 4