Aperiodic Ising Quantum Chains

TL;DR

This paper derives and refines Luck's criterion for aperiodic disorder in Ising quantum chains using an exact renormalisation approach, providing formulas for critical exponents for various substitution sequences.

Contribution

It introduces an exact renormalisation scheme for Ising quantum chains with aperiodic couplings, confirming and refining Luck's conjectures and deriving a formula for the correlation length exponent.

Findings

Luck's criterion is validated within the renormalisation framework.

An exact formula for the critical exponent is provided for two-letter substitution sequences.

The results refine the understanding of critical behavior in aperiodic quantum chains.

Abstract

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.