From 07113dc8bac1d12d74ed17e0852918c3c0696533 Mon Sep 17 00:00:00 2001 From: g-simonetti Date: Wed, 20 Aug 2025 16:18:34 +0100 Subject: [PATCH 1/2] Changed beta=3 to beta=Nc with comments --- Grid/qcd/smearing/WilsonFlow.h | 20 +++++++++++++++++--- 1 file changed, 17 insertions(+), 3 deletions(-) diff --git a/Grid/qcd/smearing/WilsonFlow.h b/Grid/qcd/smearing/WilsonFlow.h index 70b77da9..a89696ac 100644 --- a/Grid/qcd/smearing/WilsonFlow.h +++ b/Grid/qcd/smearing/WilsonFlow.h @@ -51,10 +51,16 @@ protected: 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) { - SG = (ActionBase *) new WilsonGaugeAction(3.0); - // WilsonGaugeAction with beta 3.0 + SG = (ActionBase *) new WilsonGaugeAction(Gimpl::num_colours); setDefaultMeasurements(meas_interval); } @@ -149,9 +155,17 @@ public: //////////////////////////////////////////////////////////////////////////////// // Implementations //////////////////////////////////////////////////////////////////////////////// + +//Compute t^2 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 RealD WilsonFlowBase::energyDensityPlaquette(const RealD t, const GaugeField& U){ - static WilsonGaugeAction SG(3.0); + static WilsonGaugeAction SG(Gimpl::num_colours); return 2.0 * t * t * SG.S(U)/U.Grid()->gSites(); } From 1245a8c1511cfe70104e137f468a48bdaeb2d5f9 Mon Sep 17 00:00:00 2001 From: g-simonetti Date: Wed, 20 Aug 2025 16:27:34 +0100 Subject: [PATCH 2/2] num_colours added to class S --- Grid/qcd/action/gauge/GaugeImplTypes.h | 2 ++ 1 file changed, 2 insertions(+) diff --git a/Grid/qcd/action/gauge/GaugeImplTypes.h b/Grid/qcd/action/gauge/GaugeImplTypes.h index a9af1fae..8bbcde10 100644 --- a/Grid/qcd/action/gauge/GaugeImplTypes.h +++ b/Grid/qcd/action/gauge/GaugeImplTypes.h @@ -176,6 +176,8 @@ public: Group::ColdConfiguration(pRNG, U); } + static const int num_colours = Group::Dimension; + };