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BeginPackage["Schofield`"]
β::usage = "Gives the exponent for the magnetization."
δ::usage = "Exponent."
α::usage = "Exponent."
Δ::usage = "Exponent."
$Assumptions = {θc > 0, θi > 0, θc > θi, gC[_] ∈ Reals, B > 0, γ > 0}
β[D_:2] := Piecewise[
{
{1/8, D == 2},
{0.326419, D == 3},
{1/2, D == 4},
{β, True}
}
]
δ[D_:2] := Piecewise[
{
{15, D == 2},
{4.78984, D == 3},
{3, D == 4},
{δ, True}
}
]
α[D_:2] := Piecewise[
{
{0, D == 2},
{0.11008, D == 3},
{0, D == 4},
{α, True}
}
]
Δ[D_:2] := β[D] δ[D]
f[θi_:1][n_][θ_] := (θ / θi)^2 - 1
g[gC_:gC, θc_:θc][n_][θ_] := (1 - (θ/θc)^2) Sum[gC[i] θ^(2i+1), {i, 0, n}]
I\[ScriptCapitalM]f[γ_][y_] := (1 + (1 + γ x) / x) Exp[-1/x]
R\[ScriptCapitalM]f[γ_][y_] := (1 - y - γ y) Exp[1/y] ExpIntegralEi[-1/y] / (π y)
R\[ScriptCapitalM][2][γ_, B_, θc_, M0_][θ_] := - M0 (R\[ScriptCapitalM]f[γ][B(θc - θ)] - R\[ScriptCapitalM]f[γ][B(θc + θ)])
eqLow[D_:2][f_, g_][m_] := SeriesCoefficient[
R\[ScriptCapitalM][D][γ, B, θc, M0][θ] + f[θ]^β[D] Gl'[g[θ] f[θ]^(-Δ[D])],
{θ, θc, m},
Assumptions -> Join[$Assumptions, {θ < θc, θ > θi}]
]
EndPackage[]
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