Topology, symmetry, and phase transitions in lattice gauge ... - tuprints

More documents

Recommendations

Info

50 universal aspects of confinement in 2 + 1 dimensions Figure 3.19: Critical couplings for 2 + 1 d SU(2) (N t = 4) from self-duality compared to those of Table 3.1, with N s up to 96 and the infinite-volume extrapolated result β c = 6.53658(16) shown as the narrow gray band here. N s β c (F k = F e ) β c (F k = f I (0)) 12 6.53474(42) 6.51333(33) 16 6.53627(36) 6.52508(13) 24 6.53645(17) 6.5324(14) 32 6.53672(24) 6.5346(23) w. av. N S = 24, 32 exp. (full set N s ≤ 96) 6.53654(14) 6.53658(16) Table 3.3: Comparison of N t = 4 pseudo-critical critical couplings β c (N t , N s ) for SU(2) in 2 + 1 d obtained using self-duality (with weighted mean) versus the intersection of F k with its known universal value (with infinite volume extrapolation from the full set of N s lattices). The intersections F k = F e were obtained using a simultaneous linear fit.
3.6 exploiting self-duality 51 N t ω from F k = F e offset red. χ 2 ω from β c (N t , N s ) extrap. red. χ 2 2 1.61(9) 0.78 1.34(12) 0.83 3 1.53(25) 0.36 1.16(50) 0.21 4 1.54(7) 1.52 1.47(6) 0.98 Table 3.4: SU(2) correction to scaling exponents obtained from the offset of F k = F e from the universal value f I (0) (left) and from the extrapolations of pseudo-critical couplings in Section 3.4.3, together with the reduced χ 2 of the fits that they were extracted from. comparison with the values for ω obtained as a fit parameter in our extrapolations of pseudo-critical couplings β c (N t , N s ) in Section 3.4.3 from universality alone. Exploitation of self-duality to single out the scaling correction yields a more consistent estimate for ω between various values of N t , and is therefore the preferred method.
Page 1 and 2:
T O P O L O G Y, S Y M M E T RY, A
Page 3:
To Angela.
Page 6 and 7:
Z U S A M M E N FA S S U N G Wir un
Page 8 and 9: viii contents 4.6 Algebraic formula
Page 10 and 11: 2 introduction While waiting on exp
Page 13 and 14: G A U G E T H E O R I E S 2 Before
Page 15 and 16: 2.2 quantization 7 The non-abelian
Page 17 and 18: 2.3 lattice field theory 9 Figure 2
Page 19 and 20: 2.3 lattice field theory 11 the pro
Page 21: 2.3 lattice field theory 13 picked
Page 24 and 25: 16 universal aspects of confinement
Page 73 and 74: ’ T H O O F T M O N O P O L E S I
Page 75 and 76: 4.1 magnetic charges in the continu
Page 77 and 78: 4.2 magnetic charge on the lattice
Page 79 and 80: 4.4 twisted c-periodic boundary con
Page 81 and 82: 4.5 intuitive picture 73 Therefore
Page 83 and 84: 4.5 intuitive picture 75 The constr
Page 85 and 86: 4.5 intuitive picture 77 This illus
Page 87 and 88: 4.6 algebraic formulation 79 It fol
Page 89 and 90: 4.6 algebraic formulation 81 Figure
Page 91 and 92: 4.6 algebraic formulation 83 Applyi
Page 93: 4.7 the punchline 85 this restricti
Page 96 and 97: 88 fractional electric charge and q
Page 108 and 109:
100 fractional electric charge and
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
Page 116 and 117:
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
Page 127 and 128:
C O N C L U D I N G R E M A R K S 6
Page 129 and 130:
T W I S T AWAY F R O M C R I T I C
Page 131 and 132:
twist away from criticality 123 0.1
Page 133 and 134:
Page 135:
Page 138 and 139:
130 more on c-periodic boundary con
Page 140 and 141:
Page 142 and 143:
Page 145 and 146:
L O W- E N E R G Y R E P R E S E N
Page 147 and 148:
B I B L I O G R A P H Y [1] S. Glas
Page 149 and 150:
ibliography 141 [30] L. von Smekal,
Page 151 and 152:
ibliography 143 [60] J. Engels, E.
Page 153 and 154:
ibliography 145 [89] A. S. Kronfeld
Page 155 and 156:
ibliography 147 [120] Y. Aoki, G. E
Page 157 and 158:
ibliography 149 [151] M. P. Nightin
Page 159:
ibliography 151 [179] C. Korthals A
Page 163:
C U R R I C U L U M Name: Samuel Ry
show all

Topology, symmetry, and phase transitions in lattice gauge ... - tuprints

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?