Observable

©  Prof. Dr. Jürgen Schnack, Universität Bielefeld, 30. 10. 2018

Konstanten

muBDurchkB=0.6717; (* Kelvin (Subscript[k, B])/Tesla *)
gmuBDurchkB=2.0 * 0.6717; (* Kelvin (Subscript[k, B])/Tesla *)

Feld der Eigenwerte für Spin 1/2
(Subscript[E, ν]), (Subscript[S, ν]) , (Subscript[M, ν])

TotalSpins={1/2};

EV={{0.0,0,0}};

For[m=1,m<Length[TotalSpins]+1,m++,
For[a=0,a<2*TotalSpins[[m]]+1,a++,
AppendTo[EV,{0.0,TotalSpins[[m]],TotalSpins[[m]]-a}]]]

EV=Delete[EV,1];

LengthOfEV=Length[EV];
TableForm[EV]

Plot der Energieeigenwerte gegen S

EVB0=ListPlot[Table[{EV[[i,2]],EV[[i,1]]},{i,1,LengthOfEV}],PlotStyle->{PointSize[0.03`],Red},BaseStyle->{FontFamily->Helvetica,FontSize->18},AxesLabel->{"S","E"},PlotLabel->"Energieeigenwerte"]

B1=1.`;
EVB1=ListPlot[Table[{EV[[i,2]],EV[[i,1]]+gmuBDurchkB EV[[i,3]] B1},{i,1,LengthOfEV}],PlotStyle->{PointSize[0.02`],Green},BaseStyle->{FontFamily->Helvetica,FontSize->18},AxesLabel->{"S","E"},PlotLabel->"Energieeigenwerte"]

Show[EVB0,EVB1]

Zustandssumme

Z[T_,B_]=Sum[(E^(-((EV[[m,1]]+gmuBDurchkB*B*EV[[m,3]])/T))),{m,1,LengthOfEV}]

Gibbs Freie Enthalpie

G[T_,B_]=-T*Log[Z[T,B]]

Entropie

S[T_,B_]=-Simplify[(∂_T) G[T,B]]

Enthalpie

H[T_,B_]=(T^2)*Simplify[(∂_T) Log[Z[T,B]]]

Wärmekapazität

CW[T_,B_]=Simplify[(∂_T) H[T,B]]

Plot[{CW[T,0.`],CW[T,2.`],CW[T,4.`]},{T,0.01`,10.`},PlotPoints->50,BaseStyle->{FontFamily->Helvetica,FontSize->18},PlotStyle->{Red,Green,Blue},AxesLabel->{"T","C/\!\(\*SubscriptBox[\(k\), \(B\)]\)"},PlotLabel->"Wärmekapazität"]

Magnetisierung

M[T_,B_]=-Simplify[(∂_B) G[T,B]]/muBDurchkB

Plot[{M[0.01`,B],M[0.5`,B],M[1.`,B]},{B,0.`,6.`},PlotPoints->100,BaseStyle->{FontFamily->Helvetica,FontSize->18},PlotStyle->{Red,Green,Blue},PlotRange->{0.0,1.0},AxesLabel->{"B","M/(\!\(\*SubscriptBox[\(μ\), \(B\)]\))"},PlotLabel->"Magnetisierung"]

Suszeptibilität

χ[T_,B_]=Simplify[(∂_B) M[T,B]]

Plot[{χ[0.1`,B],χ[0.5`,B],χ[1.`,B]},{B,0.`,6.`},PlotPoints->50,BaseStyle->{FontFamily->Helvetica,FontSize->18},PlotStyle->{Red,Green,Blue},AxesLabel->{"B","χ"},PlotLabel->"Suszeptilität"]

Plot[{χ[T,0.`],χ[T,1.`],χ[T,2.`]},{T,0.`,6.`},PlotPoints->100,BaseStyle->{FontFamily->Helvetica,FontSize->18},PlotStyle->{Red,Green,Blue},AxesLabel->{"T","χ"},PlotLabel->"Suszeptilität"]

Wärmekapazität über Entropie: auch o.k.

CW2[T_,B_]=T*Simplify[(∂_T) S[T,B]]

CW2[T_,B_]=Chop[T*Simplify[(∂_T) S[T,B]]]

Plot[{CW2[T,0.`],CW2[T,2.`],CW2[T,4.`]},{T,0.01`,10.`},PlotPoints->50,BaseStyle->{FontFamily->Helvetica,FontSize->18},PlotStyle->{Red,Green,Blue},AxesLabel->{"T","C/\!\(\*SubscriptBox[\(k\), \(B\)]\)"},PlotLabel->"Wärmekapazität"]