Date of Original Version
Finite‐size scaling (phenomenological renormalization) techniques are trusted and widely applied in low‐dimensional magnetism and, particularly, in lattice gauge field theory. Recently, investigations have begun which subject the theoretical basis to systematic and intensive scrutiny to determine the validity of finite‐size scaling in a variety of situations. The 2D ANNNI model is an example of a situation where finite‐size scaling methods encounter difficulty, related to the occurrence of a disorder line (one‐dimensional line). A second example concerns the behavior of the spin‐1/2 antiferromagnetic XXZ model where the T=0 critical behavior is exactly known and features an essential singularity at the isotropic Heisenberg point. Standard finite‐size scaling techniques do not convincingly reproduce the exact phase behavior and this is attributable to the essential singularity. The point is relevant in connection with a finite‐size scaling analysis of a spin‐one antiferromagnetic XXZ model, which claims to support a conjecture by Haldane that the T=0 phase behavior of integer‐spin Heisenberg chains is significantly different from that of half‐integer‐spin Heisenberg chains.
Jill C. Bonner and Gerhard Müller. Finite-size scaling and integer-spin Heisenberg chains. J. Appl. Phys. 55 (1984), 2395-2397.
Available at: http://dx.doi.org/10.1063/1.333673