2.1 dispersion relation

Here we compare the dispersion relation of the continuum E(p)2=m2+→p2 where pi=2πni/L, with the one on the lattice

coshE(p)=coshE(0)+123∑i=14sin2pi2. In terms of parameters of the lagrangian the dispersion relation looks like

coshE(p)=1+m2+123∑i=14sin2pi2. so E(0) is related to the parameter of the lagrangian m as

coshE(0)=1+m2

2.1.0.1 ../out/G2t_T48_L30_msq0-4.900000_msq1-4.650000_l02.500000_l12.500000_mu5.000000_g0.000000_rep0_output

00.050.10.150.20.150.20.250.30.350.40.45
colourcontlatticedispersion relation$p^2$$E_1(P)$
00.10.2−0.005−0.004−0.003−0.002−0.0010
lab_cont$E_1^0(p)-\sqrt{ M_0^2 + \bf{p}^2}$$E_1^0(p)-\cosh^-1\left(\cosh M_0 + \frac{1}{2}\sum_{i=1}^{3} 4 \sin^2 \frac{p_i}{2}\right)$$p^2$$E_1^0(p)-\mbox{dispersion relation}$

2.1.1 heavy mass

2.1.1.1 ../out/G2t_T32_L28_msq0-4.900000_msq1-4.650000_l02.500000_l12.500000_mu5.000000_g0.000000_rep0_output

E1_1(L28T32) = 0.44685(18) χ2/dof= 0.22457