Chaotic Spin Correlations in Frustrated Ising Hierarchical Lattices

TL;DR

This paper investigates chaotic behavior in spin correlations of frustrated hierarchical Ising models, revealing how correlations vary chaotically with distance and are sensitive to temperature and frustration changes, while thermodynamic quantities remain smooth.

Contribution

It introduces a detailed analysis of chaotic spin correlations and demonstrates the calculation of thermodynamic densities and Lyapunov exponents in such models.

Findings

Spin-spin correlations behave chaotically with distance.

Far correlations are sensitive to temperature and frustration.

Thermodynamic quantities are smooth functions of temperature.

Abstract

Spin-spin correlations are calculated in frustrated hierarchical Ising models that exhibit chaotic renormalization-group behavior. The spin-spin correlations, as a function of distance, behave chaotically. The far correlations, but not the near correlations, are sensitive to small changes in temperature or frustration, with temperature changes having a larger effect. On the other hand, the calculated free energy, internal energy, and entropy are smooth functions of temperature. The recursion-matrix calculation of thermodynamic densities in a chaotic band is demonstrated. The leading Lyapunov exponents are calculated as a function of frustration.