added new plot, made many changes

5 files changed, 127 insertions, 39 deletions

diff --git a/essential-ising.tex b/essential-ising.tex
index b7f432c..9397aa0 100644
--- a/essential-ising.tex
+++ b/essential-ising.tex
@@ -374,6 +374,14 @@ correction appears to match data quite well.
   \label{fig:scaling_fits}
 \end{figure}
 
+\begin{figure}
+  \input{fig-series}
+  \caption{
+    Something
+  }
+  \label{fig:series}
+\end{figure}
+
 Abrupt phase transitions, such as the jump in magnetization in the Ising
 model below $T_\c$, are known to imply essential singularities in the free
 energy that are usually thought to be unobservable in practice. We have
diff --git a/figs/fig-series-data.dat b/figs/fig-series-data.dat
new file mode 100644
index 0000000..b59d9e5
--- /dev/null
+++ b/figs/fig-series-data.dat
@@ -0,0 +1,100 @@
+1.	1.222409953716735	1.222409953716735	1.222409953716735	1.2224099537167044
+2.	0.012768485949999997	0.012768487260939602	0.012768487260939605	0.012768487260939603
+3.	0.0015989185962086278	0.002936926367989711	0.0029369263679897106	0.002936926367989711
+4.	0.00040044539146033526	0.0014967545682344	0.0014967545682344	0.0014967545682344006
+5.	0.00015043590579476038	0.001069611169121874	0.001166452519998439	0.0011664525199984396
+6.	0.00007535263562324922	0.0008989696219143944	0.0012114652004510606	0.0012114652004510617
+7.	0.00004717972469216129	0.0008276269886291274	0.0015642408094569038	0.0015642408094569044
+8.	0.00003544815233522661	0.0008078196901937446	0.0024082024927311986	0.002408202492731202
+9.	0.00003107267152455227	0.0008216915431728964	0.004056269379287904	0.
+10.	0.00003112830920066225	0.0008622442428432445	0.0033506342367347693	0.
+11.	0.00003508205231218031	0.0009275308272546977	0.003892074494364564	0.
+12.	0.000043931086312632846	0.001018727971066034	0.0076881916377454845	0.
+13.	0.00006051340326893378	0.0011397750090026376	0.005819482157815063	0.
+14.	0.00009093263478735651	0.0012981205968348535	0.015350797753844346	0.
+15.	0.00014803011549922843	0.0015070299640063782	0.021713357626681647	0.
+16.	0.00025951655314221373	0.001791120497207254	0.017127700862109584	0.
+17.	0.0004874648150938956	0.0021995545568045177	0.061647292622468666	0.
+18.	0.000976675306254026	0.002838525348721276	0.06960043351576076	0.
+19.	0.0020791512296463336	0.00395444310749567	0.08321853002900696	0.
+20.	0.004686466697126927	0.006155435253335119	0.15616156108858786	0.
+21.	0.011150288049494599	0.011023943805041934	0.10841846821491403	0.
+22.	0.02792563344664958	0.0228746058933135	0.30283985923063717	0.
+23.	0.07343604487451597	0.05398333614349035	0.5696973144179611	0.
+24.	0.2023107266841804	0.1406990167620353	0.9478221105144627	0.
+25.	0.582684810134423	0.39482616921973535	1.8075567233796437	0.
+26.	1.7511844376234253	1.1731136661845256	2.6435205440644234	0.
+27.	5.482250154152467	3.6550893967561557	6.91992686390437	0.
+28.	17.84921607985103	11.877736761822446	16.97204977350865	0.
+29.	60.34896995607664	40.129964425923205	50.145042504555185	0.
+30.	211.5996007415891	140.66867701824236	169.1437967742838	0.
+31.	768.4220039185923	510.78832888036214	584.3887060715731	0.
+32.	2886.74217901615	1918.823133297249	2189.2479268788884	0.
+33.	11206.155442975665	7448.672149029651	8451.814818596984	0.
+34.	44904.88322563464	29847.93321803939	33709.849559884235	0.
+35.	185564.3146203608	123343.0487120729	139188.66286439917	0.
+36.	790060.4642113362	525146.4115581461	592314.2870653236	0.
+37.	3.4627036490951697e6	2.301629179003913e6	2.5956674903515363e6	0.
+38.	1.561006732181264e7	1.0375876502243081e7	1.1701215963883355e7	0.
+39.	7.232583408762334e7	4.807435490708013e7	5.421387113851891e7	0.
+40.	3.4416285684537506e8	2.2876206682521957e8	2.579749891003154e8	0.
+41.	1.6807981282573242e9	1.1172119415933652e9	1.2598777451502264e9	0.
+42.	8.419038543072664e9	5.59606191699409e9	6.310662973902495e9	0.
+43.	4.322483111925727e10	2.8731170435750965e10	3.240004953851788e10	0.
+44.	2.273366972198791e11	1.5110873136891782e11	1.704048262724837e11	0.
+45.	1.224122702643309e12	8.136637458800464e11	9.175659426748799e11	0.
+46.	6.744730164745367e12	4.483163655852235e12	5.055648950120043e12	0.
+47.	3.800703966055813e13	2.5262949697137637e13	2.848894549121525e13	0.
+48.	2.1893178924669956e14	1.455220619190509e14	1.641047517054685e14	0.
+49.	1.2885273315436018e15	8.564729442465065e14	9.658417286189514e14	0.
+50.	7.745007150370178e15	5.148039094631592e15	5.805426792869374e15	0.
+51.	4.752310997877456e16	3.158819912225837e16	3.5621908487771484e16	0.
+52.	2.97551270339654e17	1.977797492792009e17	2.2303557421161232e17	0.
+53.	1.9002858544125407e18	1.2631035297396178e18	1.4243977053803738e18	0.
+54.	1.2373974873511565e19	8.224873801670003e18	9.275163194703055e18	0.
+55.	8.212436982919073e19	5.4587356511665684e19	6.155798279972477e19	0.
+56.	5.553320779256231e20	3.691244168221926e20	4.16260393500513e20	0.
+57.	3.824744252912394e21	2.5422743399300024e21	2.8669144301967885e21	0.
+58.	2.6821148975499934e22	1.782778515346008e22	2.0104334812390848e22	0.
+59.	1.9144286488490855e23	1.2725041225671133e23	1.434998723061887e23	0.
+60.	1.3904460060908237e24	9.242174034646032e23	1.0422369328971118e24	0.
+61.	1.0272900726620242e25	6.828308034987748e24	7.70026056270309e24	0.
+62.	7.718471276760064e25	5.1304009295398314e25	5.785536291884895e25	0.
+63.	5.895872429428827e26	3.918935279770454e26	4.419370454288003e26	0.
+64.	4.5774827690813603e27	3.0426131045091415e27	3.431144813058715e27	0.
+65.	3.6112222559045933e28	2.4003481200029584e28	2.7068646977421326e28	0.
+66.	2.8941507108016424e29	1.9237168818172808e29	2.169369214593486e29	0.
+67.	2.3557079644397923e30	1.56581865723538e30	1.7657685612415315e30	0.
+68.	1.9469389628317746e31	1.2941134463691745e31	1.459367486598489e31	0.
+69.	1.63348100950666e32	1.0857606628389791e32	1.2244087363595867e32	0.
+70.	1.3909449856148462e33	9.245490708274885e32	1.0426109530938098e33	0.
+71.	1.201838174575332e34	7.988514133055071e33	9.008621172063247e33	0.
+72.	1.0534913772398763e35	7.002465834558905e34	7.896657741748534e34	0.
+73.	9.366477294437048e35	6.225816239360912e35	7.02083254196269e35	0.
+74.	8.444923733083432e36	5.613267578070311e36	6.330063426816723e36	0.
+75.	7.7197909970564705e37	5.131278136177343e37	5.786525514931299e37	0.
+76.	7.153592759514119e38	4.7549310772801526e38	5.362120171665246e38	0.
+77.	6.718501632269003e39	4.465729777746411e39	5.0359888152484645e39	0.
+78.	6.394004976646929e40	4.2500396645178125e40	4.792755782387475e40	0.
+79.	6.165249346017175e41	4.097987780415576e41	4.621287371671692e41	0.
+80.	6.021881417425029e42	4.002692361447055e42	4.5138230404303897e42	0.
+81.	5.957255694957615e43	3.9597362041031383e43	4.465381522762211e43	0.
+82.	5.967922555790579e44	3.966826374004722e44	4.473377084092526e44	0.
+83.	6.053341122798547e45	4.0236033548165993e45	4.5374042990299425e45	0.
+84.	6.215784531727004e46	4.1315780801580665e46	4.659167042458534e46	0.
+85.	6.460423592021501e47	4.29418754223065e47	4.8425411992048355e47	0.
+86.	6.795590978710545e48	4.5169703978718155e48	5.093772694408335e48	0.
+87.	7.233243867785832e49	4.807874478280617e49	5.421824271229932e49	0.
+88.	7.789660130188514e50	5.177719543123572e50	5.838897337138516e50	0.
+89.	8.48642373535593e51	5.6408522697275565e51	6.361170593074344e51	0.
+90.	9.351781162961525e52	6.216047848201684e52	7.009816759309207e52	0.
+91.	1.0422485337917562e54	6.927735629044529e53	7.812384734230928e53	0.
+92.	1.174629092414621e55	7.807657723276689e54	8.804669992269844e54	0.
+93.	1.3385330408368046e56	8.897113056060406e55	1.0033245195801371e56	0.
+94.	1.5420692388222914e57	1.0250000515114435e57	1.1558891943626807e57	0.
+95.	1.7958653585021562e58	1.1936961315551265e58	1.3461272102206315e58	0.
+96.	2.1139201448674616e59	1.4051043901472477e59	1.584531609659763e59	0.
+97.	2.5147749949180078e60	1.671549133098101e60	1.885000471897858e60	0.
+98.	3.0231334393007486e61	2.0094505830203726e61	2.266050828089256e61	0.
+99.	3.6721127039111263e62	2.440821472801901e62	2.7525063648727253e62	0.
+100.	4.50639263448796e63	2.9953601084790524e63	3.377857764505008e63	0.
\ No newline at end of file
diff --git a/figs/fig-series.gplot b/figs/fig-series.gplot
new file mode 100644
index 0000000..bde0cae
--- /dev/null
+++ b/figs/fig-series.gplot
@@ -0,0 +1,13 @@
+
+set terminal pslatex rotate size 3.417,2.111
+
+set logscale y
+
+data = "figs/fig-series-data.dat"
+
+set xrange [0:20]
+set yrange [0.000001:10]
+set key off
+
+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
+
diff --git a/figs/fig-susmag.gplot b/figs/fig-susmag.gplot
index a639f4d..80679b6 100644
--- a/figs/fig-susmag.gplot
+++ b/figs/fig-susmag.gplot
@@ -31,44 +31,11 @@ B = Tc**2 * M0 / (16 * pi)
 C0 = 0.0255369719
 A = pi / 2 * C0 / (B**2)
 
-#c0 = -0.012384
-#lamb = 1.76962
-#A2 = pi / 2 * (C0 / Tc - c0) / B**2
-
-#c0 = 0
-#lamb = 1
-#B2 = 0.521944
-#A2 = pi / 2 * C0 / (B2**2 * Tc)
-
 n = 1
 c(i) = i == 1 ? 0.00856277   : 0
 lamb = 10.487
-B2 = B
 A2 = 1.70034
-
-#n2 = 2
-#c2(i) = i == 1 ? -0.177238   : \
-#        i == 2 ? -0.0545988  : 0
-#lamb2 = 3.14865
-#B3 = B
-#A3 = 18.8816
-
-#n = 3
-#c(i) = i == 1 ? 0.00280714  : \
-#       i == 2 ? -0.00243938 : \
-#       i == 3 ? -0.0140978  : 0
-#lamb = 12.1954
-#B2 = B
-#A2 = 0.846118
-
-#n2 = 4
-#c2(i) = i == 1 ? 0.00245324  : \
-#       i == 2 ? -0.00468448 : \
-#       i == 3 ? 0.0092602   : \
-#       i == 4 ? -0.536727   : 0
-#lamb2 = 12.6068
-#B3 = B
-#A3 = 0.88157
+B2 = B
 
 n2 = 5
 c2(i) = i == 1 ? 0.00639522  : \
@@ -77,8 +44,8 @@ c2(i) = i == 1 ? 0.00639522  : \
         i == 4 ? 4.39278     : \
         i == 5 ? -56.1389    : 0
 lamb2 = 13.2489
-B3 = B
 A3 = 1.91747
+B3 = B
 
 susfunc = "figs/fig-sus_scaling-func.dat"
 magfunc = "figs/fig-mag_scaling-func.dat"
@@ -99,7 +66,7 @@ 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 / B2):(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 / B2):(-10**3 * (sum[i=1:7] GC(i + 1) * i * (i + 1) * (10**$1 / B2)**(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):(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
 
 set bmargin -1
 set tmargin 0.2
@@ -138,5 +105,5 @@ 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)) / B2) 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)):(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
 
diff --git a/makefile b/makefile
index 32f4b74..a04aaa6 100644
--- a/makefile
+++ b/makefile
@@ -1,8 +1,8 @@
 
 DOC=essential-ising
-FIGS=fig-susmag
+FIGS=fig-susmag fig-series
 DATA=data_square-4096
-FUNCS=fig-mag_scaling-func fig-sus_scaling-func
+FUNCS=fig-mag_scaling-func fig-sus_scaling-func fig-series-data
 
 all: ${DOC}.pdf