Opis użytych oznaczeń:
h - grubość warstwy magnetycznej
σ - 
w =  α \(TraditionalForm\`\(\(=\)\(h\/\(\(d\_-\) + \(d\_+\)\)\)\)\)
m = β = \(TraditionalForm\`\(\(d\_+\) - \(d\_-\)\)\/\(\(d\_+\) + \(d\_-\)\)\) 
ED - energia odmagnesowania
M- magnetyzacja nasycenia
H - zewnętrzne pole

F[w_, m_]  =  
      (1/2) (m^2) + (2/((π^3) 
                w)) (∑_(n = 1)^∞)((1/(n^3)) Sin[((π n (1 + m))/2)]^2 (1 - (E^(-2 π n w))))

Energia odmagnesowania

ED[w_, 
        m_]  =  4 Pi h (M^2) F

Wyznaczamy sigmę

sig  = 
      Solve[l  ==  (σ/(4  π (M^2))), σ]

Energia ściany domenowej

Esd[w_, m_] =  
      2 σ w  - H m M h  + 
          ED[w, m] /. σ -> 4 l (M^2) π

EE[w_, m_]  = 
      Simplify[Esd[w, m]/(4 Pi h (M^2))]

Pochodna Esd po alfa

f1[w_, m_]  = D[EE[w, m] /. F -> F[w, m], w]

p1  =  Solve[f1[w, m] == 0 /. l/h  -> a, a]

Pochodna Esd po beta

f2[w_, m_] =  D[EE[w, m] /. F -> F[w, m], m]

p2 =  Solve[f2[w, m] == 0 /. H/M/Pi -> b, b]

lh[m_, w_]  = p1[[1, 1, 2]]

rys1[x_]  :=  
      FindRoot[lh[0, w] == x, {w, x, 0, 10}, 
        MaxIterations -> 200]

w /. rys1[ .001]

lhdata  =  
        Table[{x, rys1[x][[1, 2]]}, {x, 0.001, 
            0.37,  .01}];

Wyrysowanie wprost

\(Plot[lh[0, x], {x, 0, 1.4}, PlotRange -> {{0, 1.4}, All}, 
      FrameLabel -> {"α", ""}, 
      GridLines -> Automatic, Frame -> True, 
      RotateLabel -> False, 
      PlotStyle -> {Text[\*""\!\(l\/h\)"", {0.05, 4.7}], 
          RGBColor[1, 0, 0], Thickness[0.005]}]\)

\(\(ListPlot[lhdata, PlotJoined -> True, 
        FrameLabel -> {"α", \*""\!\(l\/h\)""}, 
        GridLines -> Automatic, Frame -> True, 
        RotateLabel -> False, 
        PlotStyle -> {RGBColor[0, 0, 0], 
            Thickness[0.005]}];\)\)

Hg[m_, w_]  =  p2[[1, 1, 2]]/4

rys2[x_, 
        h_]:=FindRoot[{lh[m, w] == x, Hg[m, w] == h}, {m, 
          0}, {w, w /. rys1[x]}, 
        MaxIterations -> 200]

c  = rys2[0.1, 0.1]

rys2a[
        x_]:=FindRoot[{lh[ .9999, w] == x, 
          Hg[0.9999, w] == h}, {h, 0.2}, {w, w /. rys1[x]}, 
        MaxIterations -> 200]

ww1  =  rys2a[1/80]

wyk[hl_]  :=  
        Block[{xmax}, 
xmax  =  
            Re[rys2a[hl][[1, 2]]]; 
 
          data =  Table[{x, rys2[hl, x]}, {x, 0.001, xmax + xmax/30, 
                xmax/30}]
];

dane01 = wyk[1/1000];
dane02 = wyk[1/80];
dane03 = wyk[1/12];
dane04 = wyk[1/4];

Save["dane.dat", dane01, dane02, dane03, dane04]

dane1 =  
        Table[{dane01[[i, 1]], Re[dane01[[i, 2, 1, 2]]]}, {i, 1, 
            Length[dane01]}];
dane2 =  
        Table[{dane02[[i, 1]], Re[dane02[[i, 2, 1, 2]]]}, {i, 1, 
            Length[dane02]}];
dane3 =  
        Table[{dane03[[i, 1]], Re[dane03[[i, 2, 1, 2]]]}, {i, 1, 
            Length[dane03]}];
dane4 =  
        Table[{dane04[[i, 1]], Re[dane04[[i, 2, 1, 2]]]}, {i, 1, 
            Length[dane04]}];

pic1 = ListPlot[dane1,PlotJoined -> True,\(FrameLabel -> {\*""\!\(\(H\_*\)\)"", "m"}\),DisplayFunction -> Identity,GridLines -> Automatic,Frame -> True,RotateLabel -> False,PlotStyle -> {RGBColor[0, 0, 0], 
                Thickness[0.005]}];
pic2 = ListPlot[dane2,PlotJoined -> True,\(FrameLabel -> {\*""\!\(\(H\_*\)\)"", "m"}\),DisplayFunction -> Identity,GridLines -> Automatic,Frame -> True,RotateLabel -> False,PlotStyle -> {RGBColor[1, 0, 0], 
                Thickness[0.005]}];
pic3 = ListPlot[dane3,PlotJoined -> True,\(FrameLabel -> {\*""\!\(\(H\_*\)\)"", "m"}\),DisplayFunction -> Identity,GridLines -> Automatic,Frame -> True,RotateLabel -> False,PlotStyle -> {RGBColor[0, 1, 0], 
                Thickness[0.005]}];
pic4 = ListPlot[dane4,PlotJoined -> True,\(FrameLabel -> {\*""\!\(\(H\_*\)\)"", "m"}\),DisplayFunction -> Identity,GridLines -> Automatic,Frame -> True,RotateLabel -> False,PlotStyle -> {RGBColor[0, 0, 1], 
                Thickness[0.005]}];

\(\(Show[
        gra1\  = 
          Graphics[{Text[\*""\!\(l\/h\)=\!\(1\/4\)"", {0.3,  .9}], 
              Text[\*""\!\(l\/h\)=\!\(1\/12\)"", {0.53,  .9}], 
              Text[\*""\!\(l\/h\)=\!\(1\/80\)"", {0.763,  .87}], 
              Text[\*""\!\(l\/h\)=0"", {0.88,  .85}]}], 
        DisplayFunction -> Identity];\)\)

Show[pic1, pic2, pic3, pic4, gra1, 
        DisplayFunction -> $DisplayFunction, 
        PlotRange -> {{0, Automatic}, {0, Automatic}}];

Solve[{m  == ((d1 - d2)/(d1 + d2)), w  == (h/(d1 + d2))}, {d1, d2}] // Simplify

h  = 80;
daneDD1 =  
        Table[{dane02[[i, 1]], 1/Re[dane02[[i, 2, 2, 2]]]}, {i, 1, 
            Length[dane02]}];
daneDD2 =  
        Table[{dane02[[i, 1]],  (1 + Re[dane02[[i, 2, 1, 2]]])/
                2/Re[dane02[[i, 2, 2, 2]]]}, {i, 1, 
            Length[dane02]}];
daneDD3 =  
        Table[{dane02[[i, 
                1]], - (-1 + Re[dane02[[i, 2, 1, 2]]])/
                2/Re[dane02[[i, 2, 2, 2]]]}, {i, 1, 
            Length[dane02]}];

picDD1 = ListPlot[daneDD1,PlotJoined -> True,\(FrameLabel -> {\*""\!\(\(H\_*\)\)"", "" (*\(,\)\("(d+)+(d-)"\)*) }\),RotateLabel -> False,DisplayFunction -> Identity,GridLines -> Automatic,Frame -> True,PlotStyle -> {RGBColor[0, 0, 0], 
                  Thickness[0.005]}];picDD2 = ListPlot[daneDD2,PlotJoined -> True,\(FrameLabel -> {\*""\!\(\(H\_*\)\)"", "" (*\(,\)\("(d+)"\)*) }\),RotateLabel -> False,DisplayFunction -> Identity,GridLines -> Automatic,Frame -> True,PlotStyle -> {RGBColor[1, 0, 0], 
                  Thickness[0.005]}];
picDD3 = ListPlot[daneDD3,PlotJoined -> True,\(FrameLabel -> {\*""\!\(\(H\_*\)\)"", "" (*\(,\)\("(d-)"\)*) }\),RotateLabel -> False,DisplayFunction -> Identity,GridLines -> Automatic,Frame -> True,PlotStyle -> {RGBColor[0, 1, 0], 
                Thickness[0.005]}];

\(\(Show[
        gra2a\  = 
          Graphics[{Text[\*""\!\(\(d\_+\)\)+\!\(\(d\_-\)\)"", {0.35,  .8}], Text[\*""\!\(\(d\_+\)\)"", {0.53,  .6}], 
              Text[\*""\!\(\(d\_-\)\)"", {0.53,  .2}], 
              Text[\*""(l/h)=(1/80)"", {0.05, 1.6}]}], 
        DisplayFunction -> Identity];\)\)

Show[picDD1, picDD2, picDD3, gra2a, 
      PlotRange -> {{0, 0.72}, {0, Automatic}}, 
      DisplayFunction -> $DisplayFunction]

h  = 12;
daneDD1a =  
        Table[{dane03[[i, 1]], 1/Re[dane03[[i, 2, 2, 2]]]}, {i, 1, 
            Length[dane03]}];
daneDD2a =  
        Table[{dane03[[i, 1]],  (1 + Re[dane03[[i, 2, 1, 2]]])/
                2/Re[dane03[[i, 2, 2, 2]]]}, {i, 1, 
            Length[dane03]}];
daneDD3a =  
        Table[{dane03[[i, 
                1]], - (-1 + Re[dane03[[i, 2, 1, 2]]])/
                2/Re[dane03[[i, 2, 2, 2]]]}, {i, 1, 
            Length[dane03]}];

picDD1a = ListPlot[daneDD1a,PlotJoined -> True,\(FrameLabel -> {\*""\!\(\(H\_*\)\)"", ""}\),RotateLabel -> False,DisplayFunction -> Identity,GridLines -> Automatic,Frame -> True,PlotStyle -> {RGBColor[0, 0, 0], 
                  Thickness[0.005]}];picDD2a = ListPlot[daneDD2a,PlotJoined -> True,RotateLabel -> False,\(FrameLabel -> {\*""\!\(\(H\_*\)\)"", ""}\),DisplayFunction -> Identity,GridLines -> Automatic,Frame -> True,PlotStyle -> {RGBColor[1, 0, 0], 
                  Thickness[0.005]}];
picDD3a = ListPlot[daneDD3a,PlotJoined -> True,RotateLabel -> False,\(FrameLabel -> {\*""\!\(\(H\_*\)\)"", ""}\),DisplayFunction -> Identity,GridLines -> Automatic,Frame -> True,PlotStyle -> {RGBColor[0, 1, 0], 
                Thickness[0.005]}];

\(\(gra2b\  = 
        Graphics[{Text[\*""\!\(\(d\_+\)\)+\!\(\(d\_-\)\)"", {0.25, 
                2.2}], Text[\*""\!\(\(d\_+\)\)"", {0.35, 1.6}], 
            Text[\*""\!\(\(d\_-\)\)"", {0.35,  .7}], 
            Text[\*""\!\(l\/h\)=\!\(1\/12\)"", {0.05, 
                4.5}]}];\)\)
Show[picDD1a, picDD2a, picDD3a, gra2b, 
        PlotRange -> {{0, 0.46}, {0, Automatic}}, 
        DisplayFunction -> $DisplayFunction];

dane1b =  
        Table[{dane01[[i, 1]], Re[dane01[[i, 2, 2, 2]]]}, {i, 1, 
            Length[dane01]}];
dane2b =  
        Table[{dane02[[i, 1]], Re[dane02[[i, 2, 2, 2]]]}, {i, 1, 
            Length[dane02]}];
dane3b =  
        Table[{dane03[[i, 1]], Re[dane03[[i, 2, 2, 2]]]}, {i, 1, 
            Length[dane03]}];
dane4b =  
        Table[{dane04[[i, 1]], Re[dane04[[i, 2, 2, 2]]]}, {i, 1, 
            Length[dane04]}];

\(\(pic1b\  = \ 
        ListPlot[dane1b, PlotJoined -> True, 
          FrameLabel -> {\*""\!\(\(H\_*\)\)"", "α"}, 
          DisplayFunction -> Identity, GridLines -> Automatic, 
          Frame -> True, 
          PlotStyle -> {RGBColor[0, 0, 0], 
              Thickness[0.005]}];\)\)
\(\(pic2b\  = \ 
        ListPlot[dane2b, PlotJoined -> True, 
          FrameLabel -> {\*""\!\(\(H\_*\)\)"", "α"}, 
          DisplayFunction -> Identity, GridLines -> Automatic, 
          Frame -> True, 
          PlotStyle -> {RGBColor[1, 0, 0], 
              Thickness[0.005]}];\)\)
\(\(pic3b\  = \ 
        ListPlot[dane3b, PlotJoined -> True, 
          FrameLabel -> {\*""\!\(\(H\_*\)\)"", "α"}, 
          DisplayFunction -> Identity, GridLines -> Automatic, 
          Frame -> True, 
          PlotStyle -> {RGBColor[0, 1, 0], 
              Thickness[0.005]}];\)\)
\(\(pic4b\  = \ 
        ListPlot[dane4b, PlotJoined -> True, 
          FrameLabel -> {\*""\!\(\(H\_*\)\)"", "α"}, 
          DisplayFunction -> Identity, GridLines -> Automatic, 
          Frame -> True, 
          PlotStyle -> {RGBColor[0, 0, 1], 
              Thickness[0.005]}];\)\)

\(\(Show[
        gra3\  = 
          Graphics[{Text[\*""\!\(l\/h\)=\!\(1\/4\)"", {0.3,  .25}], 
              Text[\*""\!\(l\/h\)=\!\(1\/12\)"", {0.5,  .6}], 
              Text[\*""\!\(l\/h\)=\!\(1\/80\)"", {0.76,  .7}], 
              Text[\*""\!\(l\/h\)=0"", {0.88, 1.7}]}], 
        DisplayFunction -> Identity];\)\)

Show[pic1b, pic2b, pic3b, pic4b, gra3, 
        DisplayFunction -> $DisplayFunction, 
        PlotRange -> {{0, Automatic}, {0, Automatic}}];

(∑_(n = 1)^∞) Cos[π×n]/n×(1 - 
            Exp[-2 π n alf])

s3[alf_] := -Log[2] + Log[1 + (E^(-2 alf π))]

chi0[alf_] := (1/(1 + s3[alf]/(π alf)))

\(\(r3 = 
        Plot[chi0[alf], {alf, 0.0001, 10}, 
          FrameLabel -> {\*""(l/h)"", \*""(Subscript[chi, 0])""}, GridLines -> Automatic, Frame -> True, 
          RotateLabel -> False, 
          PlotStyle -> {RGBColor[0, 0, 1], 
              Thickness[0.005]}];\)\)