Aperiodic Ising Quantum Chains

Details Aperiodic Ising Quantum Chains Aperiodic Ising Quantum Chains

1997-06-11

arxiv.org/abs/cond-mat/9706106v3

J. Phys. A: Math. Gen. 30 (1997) 7315-7335

Physics

Condensed Matter

Statistical Mechanics

27 pages, LaTeX, 1 Postscript figure included, using epsf.sty and amssymb.sty (one error corrected, some minor changes)

Scientific paper

10.1088/0305-4470/30/21/009

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 renormalisation 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.

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