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Diffstat (limited to 'schofield.wl')
-rw-r--r-- | schofield.wl | 54 |
1 files changed, 54 insertions, 0 deletions
diff --git a/schofield.wl b/schofield.wl new file mode 100644 index 0000000..fdb76e3 --- /dev/null +++ b/schofield.wl @@ -0,0 +1,54 @@ + +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[] + |