On the finite-size scaling in quantum critical phenomena

N.S. Tonchev

Physica A: Statistical Mechanics and its Applications, 1991, vol. 171, issue 2, 374-383

Abstract: An exactly solvable d-dimentional model of a structural phase transition, confined to a geometry Ld−d× ∞d are subjected to periodic boundary conditions, is considered in the low-temperature region. It is shown that in this region quantum effects are essential and that borderline dimensionalities between which finite-size scaling holds do not coincide with the lower and upper critical dimensionalities for the bulk system. A generalized version of the dimensional cross-over rule is established, i.e., the finite-size scaling behaviour of a d-dimensional system finite in d∗ = d−d' directions in the quantum limit is equivalent to the finite-size scaling behaviour of the classical (d + 1)-dimensional system, also finite in d∗ directions.

Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:171:y:1991:i:2:p:374-383

DOI: 10.1016/0378-4371(91)90284-J

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