Joachim Hermisson et al 1997 J. Phys. A: Math. Gen. 30 7315 doi:10.1088/0305-4470/30/21/009
Aperiodic Ising quantum chains
Joachim Hermisson
, Uwe Grimm
and Michael Baake
Some years ago, Luck proposed a relevance criterion for the effect of aperiodic disorder on the critical behaviour of ferromagnetic Ising systems. In this article, we show how Luck's criterion can be derived within an exact renormalization scheme for Ising quantum chains with coupling constants modulated according to substitution rules. Luck's conjectures for this case are confirmed and refined. Among other outcomes, we give an exact formula for the correlation length critical exponent for arbitrary two-letter substitution sequences with marginal fluctuations of the coupling constants.
- PACS
-
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
05.70.Jk Critical point phenomena
05.10.Cc Renormalization group methods
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
- MSC
-
82B30 Statistical thermodynamics (See also 80-XX)
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.)
- Subjects
- Dates
-
Issue 21 (7 November 1997)
Received 13 June 1997, in final form 28 July 1997
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Aperiodic Ising quantum chains
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