Contents
0 Backgroun d o f th e proble m 1
0.1 Statistica l mechanic s 1
0.2 Solvabl e model s 6
1 Th e spi n 1/2 XX Z mode l fo r A - 1 1
1.1 Quantu m Hamiltonia n 1
1.2 Thre e region s i n A 13
1.3 Th e anisotropi c limi t 14
1.4 On e poin t functio n (vac|cr f |vac) 16
2 Th e six-verte x mode l i n th e anti-ferroelectri c regim e 19
2.1 Verte x mode l 19
2.2 Groun d state s an d low-temperatur e expansio n 2
2.3 Th e correlatio n functio n 2 3
2.4 Transfe r matri x 2 4
3 Solvabilit y an d Symmetr y 2 7
3.1 Commutin g Hamiltonian s 2 7
3.2 Yang-Baxte r equatio n 2 8
3.3 Z-invarian t lattic e 2 9
3.4 Quantu m affin e algebr a U q(sl2) 3 4
3.5 R matri x a s an intertwine r 3 7
3.6 Dua l module s an d crossin g symmetr y 3 9
3.7 Abelia n an d non-abelia n Symmetrie s 4 2
4 Correlatio n functions—physica l derivatio n 4 5
4.1 Corne r Transfe r Matri x 4 5
4.2 Propertie s o f Vertex Operator s 5 0
4.3 Th e on e point functio n 5 7
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