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Changed beta=3 to beta=Nc with comments

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g-simonetti
2025-08-20 16:18:34 +01:00
parent a3420e6fa9
commit 07113dc8ba
1 changed files with 17 additions and 3 deletions
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20
Grid/qcd/smearing/WilsonFlow.h
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@@ -51,10 +51,16 @@ protected:
public: public:
//Define the action used to evolve the plaquettes
//(Lüscher: https://arxiv.org/pdf/1006.4518 eq. 1.4)
//V'(t) = -g^2 * ( d/dVt S[Vt](g) ) * Vt
// = -g^2 * ( d/dVt (1/g^2 * sum_p Re tr{ 1 - Vt(p) } ) ) * Vt
// = - d/dVt ( sum_p ( Nc - Re tr Vt(p) ) * Vt
// = - d/dVt ( Nc * sum_p ( 1 - Re tr Vt(p)/Nc ) ) * Vt
// = - d/dVt SG[Vt](Nc) * Vt
explicit WilsonFlowBase(unsigned int meas_interval =1) { explicit WilsonFlowBase(unsigned int meas_interval =1) {
SG = (ActionBase *) new WilsonGaugeAction<Gimpl>(3.0); SG = (ActionBase *) new WilsonGaugeAction<Gimpl>(Gimpl::num_colours);
// WilsonGaugeAction with beta 3.0
setDefaultMeasurements(meas_interval); setDefaultMeasurements(meas_interval);
} }
@@ -149,9 +155,17 @@ public:
//////////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////////////////
// Implementations // Implementations
//////////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////////////////
//Compute t^2 <E(t)> for time from the plaquette form
//(Lüscher: https://arxiv.org/pdf/1006.4518 eq. 3.1)
//E(t) = 2 * sum_p Retr{ 1 - Vt(p) } =
// = 2 * sum_p ( Nc - Retr Vt(p) ) =
// = 2 * Nc * sum_p ( 1 - Retr Vt(p)/Nc )
// = 2 * SG[Vt](Nc)
//We divide by the volume to get an energy density per site, as is convention
template <class Gimpl> template <class Gimpl>
RealD WilsonFlowBase<Gimpl>::energyDensityPlaquette(const RealD t, const GaugeField& U){ RealD WilsonFlowBase<Gimpl>::energyDensityPlaquette(const RealD t, const GaugeField& U){
static WilsonGaugeAction<Gimpl> SG(3.0); static WilsonGaugeAction<Gimpl> SG(Gimpl::num_colours);
return 2.0 * t * t * SG.S(U)/U.Grid()->gSites(); return 2.0 * t * t * SG.S(U)/U.Grid()->gSites();
} }