Order by disorder up to arbitrarily high temperature

Ravish Mehta

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arXiv · 2604.28026

Order by disorder up to arbitrarily high temperature

Ravish Mehta

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Abstract

We prove that a class of classical lattice models on $\mathbb{Z}^d$ ($d \geq 2$) with on-site space $\mathbb{N}_0$ and nearest neighbour interaction, exhibits long-range checkerboard order at sufficiently high temperature. The ordering mechanism is purely entropic. The class of models contains the recently introduced model of Han--Huang--Komargodski--Lucas--Popov (arXiv:2503.22789), by which our work is inspired. The proof uses Pirogov--Sinai theory and the key input is a Peierls bound.

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Ravish Mehta. 2026-04-30. Order by disorder up to arbitrarily high temperature. https://arxiv.org/abs/2604.28026

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