Classical spin model shows stable states in two dimensions

A thermally and perturbatively stable classical spin model in two dimensions

Information Theory

Summary

Some materials can be thought of as tiny magnets arranged on a flat surface, where their interactions determine how the whole system behaves. Usually, these systems are sensitive to both temperature changes and small tweaks in their energy rules, causing instability. The authors build on previous work to show a model in two dimensions where many stable arrangements exist even when the temperature is above absolute zero and when the energy rules are changed a little. Their approach uses a mathematical technique called cluster expansion repeatedly to prove this stability. This is the first known example of such a robust classical spin system.

What this means in practice

  • For statistical physicists: Use the proven stable 2D classical spin model to explore robustness of metastable states against temperature and perturbations.
  • For mathematical physicists: Incorporate the recursive cluster expansion proof method to analyze stability properties in related lattice models.

A theory result. No direct application yet.

Authors

Shankar Balasubramanian, Margarita Davydova, Ting-Chun Lin, Ryan Thorngren

Abstract

We show that the 2D classical spin model constructed in arXiv:2605.10943 hosts many metastable states at non-zero temperature which are stable to arbitrary Hamiltonian perturbations, providing the first such example. Our proof relies on a recursive application of the cluster expansion.
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