Exact universal amplitude ratios for two-dimensional Ising models and a quantum spin chain

• Published in: Physical review letters Vol. 86; no. 22; p. 5160
• Main Authors: Izmailian, N S, Hu, C K
• Format: Journal Article
• Language: English
• Published: United States 28.05.2001
• ISSN: 0031-9007
• DOI: 10.1103/physrevlett.86.5160

Let f(N) and xi(-1)(N) represent, respectively, the free energy per spin and the inverse spin-spin correlation length of the critical Ising model on a N x infinity lattice, with f(N)-->f(infinity) as N-->infinity. We obtain analytic expressions for a(k) and b(k) in the expansions N( f(N)-f(infinity)) = SUM (k = 1)(infinity)a(k)/N(2k-1) and xi(-1)(N) = SUM (k = 1)(infinity)b(k)/N(2k-1) for square, honeycomb, and plane-triangular lattices, and find that b(k)/a(k) = (2(2k)-1)/(2(2k-1)-1) for all of these lattices, i.e., the amplitude ratio b(k)/a(k) is universal. We also obtain similar results for a critical quantum spin chain and find that such results could be understood from a perturbated conformal field theory.