Computational Physics

15.4 Algorithms for lattice field theories 483 g( r) 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 8 × 8 12 × 12 16 × 16 24 × 24 r Figure ...

484 Computational methods for lattice field theories Table 15.1. Values of the renormalised mass. Lm g mRa mRb 8 0.2 0.04 0.374( ...

15.4 Algorithms for lattice field theories 485 Table 15.2. Values of the renormalised mass and coupling constant. Lm g mR mR 8 0 ...

486 Computational methods for lattice field theories steps and so on [ 13 – 16 ]. The exact dynamical trajectory plus the moment ...

15.4 Algorithms for lattice field theories 487 The procedure can be implemented straightforwardly. The equations of motion in th ...

488 Computational methods for lattice field theories trajectory as exp(−SD[φ]), where the actionSDdiffers by some power ofhfrom ...

15.4 Algorithms for lattice field theories 489 From this, it follows immediately that the modified detailed balance condition ho ...

490 Computational methods for lattice field theories 〈HMD〉: 〈HMC〉= 0 = ∑ {,P}Pacc∑(HMD)HMD {,P} . (15.73) UsingPacc=min[1, ...

15.5 Reducing critical slowing down 491 Implementation All the MD algorithms described can be implemented without difficulty. Th ...

492 Computational methods for lattice field theories is a special case, but we treat them in this chapter because the ideas behi ...

15.5 Reducing critical slowing down 493 In the SW method, any configuration can be reached from any other configuration, because ...

494 Computational methods for lattice field theories Pd(S)=exp(− 2 βJ)respectively and we have T(S→S′) T(S′→S) = Tf(S→S′)[ 1 −ex ...

15.5 Reducing critical slowing down 495 IF (Frozen(x,y,x,y−1)) THEN BackTrack(x,y−1); END IF END BackTrack. Frozen(x1,y1,x2,y2) ...

496 Computational methods for lattice field theories wherescis the spin value of clusterc. We can write this as χ= 1 L^2 d 〈 ∑ c ...

15.5 Reducing critical slowing down 497 It will be clear that the cluster generated in this way is a SW cluster and therefore th ...

498 Computational methods for lattice field theories correlation timeτWexpressed in SW time steps: τW= ̄τW 〈N1C〉 Ld . (15.89) Th ...

15.5 Reducing critical slowing down 499 u u s s' s s' Figure 15.2. Spin flips in the Wolff algorithm for theO( 3 )model. formula ...

500 Computational methods for lattice field theories curves (in two dimensions, and (hyper)surfaces in higher dimensions) on whi ...

15.5 Reducing critical slowing down 501 Figure 15.3. A pair of vortices, one with positive and one with negative vorticity. Figu ...

502 Computational methods for lattice field theories free energy which is needed to change the orientation of the spins on the r ...