Aperiodic spin chain in the mean-field approximation

TL;DR

This paper studies the critical properties of an aperiodic Fibonacci spin chain using mean-field Ginzburg-Landau theory, revealing continuously varying critical exponents and estimating the upper critical dimension.

Contribution

It provides a detailed analysis of surface and bulk critical exponents in an aperiodic spin chain within the mean-field approximation, focusing on the Fibonacci sequence.

Findings

Critical exponents vary continuously with perturbation amplitude.

Surface and bulk critical properties are characterized for the Fibonacci sequence.

Upper critical dimension estimated using hyperscaling relations.

Abstract

Surface and bulk critical properties of an aperiodic spin chain are investigated in the framework of the $\phi^4$ phenomenological Ginzburg-Landau theory. According to Luck's criterion, the mean field correlation length exponent $\nu=1/2$ leads to a marginal behaviour when the wandering exponent of the sequence is $\omega=-1$. This is the case of the Fibonacci sequence that we consider here. We calculate the bulk and surface critical exponents for the magnetizations, critical isotherms, susceptibilities and specific heats. These exponents continuously vary with the amplitude of the perturbation. Hyperscaling relations are used in order to obtain an estimate of the upper critical dimension for this system.