What question did this study set out to answer?

The aim is to analyze magnetization fluctuations in Ising models on Erdős–Rényi random graphs under various conditions of edge probability.

Fluctuations of the magnetization for Ising models on Erdős–Rényi random graphs—the regimes of small p and the critical temperature*

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Randomized trial explores magnetization behavior in Ising models on Erdős–Rényi graphs, indicating phase transitions.

The aim is to analyze magnetization fluctuations in Ising models on Erdős–Rényi random graphs under various conditions of edge probability.
Proved a quenched central limit theorem for magnetization in high-temperature regime with pN → ∞.
Demonstrated a non-standard central limit theorem at critical temperature where p4N3 → ∞.
Obtained a Gaussian limiting distribution for magnetization when p4N3 → 0.
At high temperatures, observed a quenched central limit theorem for large edge probabilities.
Identified a Gaussian component in magnetization at critical temperature involving a significant term as p approaches a specific value.
Showed a phase transition at β = 1 for fluctuations of magnetization based on edge probabilities.

Kabluchko et al. (2020) studied this question.

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