On the nature of the spin glass transition

Gesualdo Delfino

doi:10.1088/1742-5468/ae5a20

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arXiv · 2511.20163

On the nature of the spin glass transition

Gesualdo Delfino

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Abstract

We recently showed that the two-dimensional Ising spin glass allows for a line of renormalization group fixed points which explains properties observed in numerical studies. We observe that this exact result corresponds to enhancement to a one-generator continuous internal symmetry. This finally explains why no finite temperature transition to a spin glass phase is observed in two dimensions. In more than two dimensions, instead, the continuous symmetry can be broken spontaneously and yields a spin glass order parameter which, for fixed temperature and disorder strength, takes continuous values in an interval. Such a feature is shared by the order parameter of the known mean field solution of the model with infinite-range interactions, which corresponds to infinitely many dimensions.

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Gesualdo Delfino. 2025-11-25. On the nature of the spin glass transition. https://doi.org/10.1088/1742-5468/ae5a20

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