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Physica A Statistical Mechanics and its Applications

Finite-size scaling and the isotropic spin-one antiferromagnetic chain

Henk W. J. Blöte, Hans W. Capel

Published Dec 1, 1986• 29 citations
Publisher
DOI
10.1016/0378-4371(86)90127-5

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Finite-size scaling calculations for deformable Heisenberg chains with spin value S=(1/2, 1, (3/2, and 2 indicate that as far as the spin-Peierls transition is concerned, the model with any spin S>(1/2 behaves differently from the S=(1/2 situation. For S=(1/2 the ground state of the isotropic antiferromagnetic or planar models is dimerized, irrespective of the strength of the elastic constant. On the other hand, from the extrapolation of finite-chain results it seems that for any higher-spin value the dimerized and uniform phases are separated by a finite critical value of the elastic constant, and the transition is discontinuous.

Physical review. B, Condensed matter•Apr 1, 1988•8 citations
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.
Ground state properties of finite anisotropic antiferromagnetic Heisenberg chains are studied for odd half-integer spins S= 1 / 2 , 3 / 2 ... as well as integer spins S=1, 2 .... Finite size scaling analysis of the results clearly distinguishes the half-integer (S= 1 / 2 , 3 / 2 ) from the integer (S=1) spin situation. It gives strong support to a recent conjecture which postulates that the T=0 phase structure is very different in the two cases. According to this idea there exists a new phase between the planar and the antiferromagnetic region, for integer spins only. This phase, which includes the isotropic point, has a finite energy gap and no long range order.
Finite-size scaling calculations for deformable Heisenberg chains with spin value S=(1/2, 1, (3/2, and 2 indicate that as far as the spin-Peierls transition is concerned, the model with any spin S>(1/2 behaves differently from the S=(1/2 situation. For S=(1/2 the ground state of the isotropic antiferromagnetic or planar models is dimerized, irrespective of the strength of the elastic constant. On the other hand, from the extrapolation of finite-chain results it seems that for any higher-spin value the dimerized and uniform phases are separated by a finite critical value of the elastic constant, and the transition is discontinuous.