High temperature modulations, meso-scale interactions and hyperscaling breakdown in Ising models with frustration: some insights from thermodynamic geometry

TL;DR

This paper investigates the phase behavior of the frustrated Axial Third Nearest Neighbour Ising chain using microscopic and macroscopic tools, revealing phenomena like hyperscaling breakdown and the role of thermodynamic curvature in understanding frustration effects.

Contribution

It introduces a combined approach using correlation functions and thermodynamic curvature to analyze frustration-induced phenomena in Ising models, highlighting new insights into high-temperature behavior.

Findings

Identification of hyperscaling breakdown in frustrated Ising chains

Thermodynamic curvature $R_0$ distinguishes ground state phase regions

Correlation length measures clarified in high-temperature modulated regimes

Abstract

In this work we revisit the Axial Third Nearest Neighbour Ising (A3NNI) chain and examine in detail some aspects of its phase behaviour ensuing from competing interactions and resulting frustration. We probe the phase behaviour with two complimentary tools: a microscopic two-point correlation function $\mathcal{C}(n)$ which we carefully construct after appropriate spin transformations, and a macroscopic, thermodynamic curvature $R$ which we obtain from the free entropy. We report novel observations of phenomena such as hyperscaling breakdown and intermediate-ranged modulations among others. The zero field thermodynamic curvature $R_0$ is shown to systematically sub-divide the ground state phases into regions of attractive or repulsive effective interactions of varying strength. Furthermore, $R_0$ brings forth the significance of some third order moments in describing the effects of frustration, including the multiphase lines. Combined use of both the probes in the short-ranged modulated order regime confirms and further clarifies the discussion in [1] regarding the appropriate measure of high temperature correlation length in this regime.