Infinite loops in higher-dimensional Lorentz mirror models

Establish whether the higher-dimensional Lorentz mirror model on Z^d has infinite loops for sufficiently small mirror probability p when d\ge3.

Background

The paper notes that the Lorentz mirror model has higher-dimensional analogues. Existing results establish only partial dynamical information in dimensions at least four, while the existence of infinite loops for small mirror density is explicitly presented as a conjecture for dimensions at least three.

References

The mirror model has higher-dimensional analogues; for d\ge3 it is conjectured that there are infinite loops for p small enough.

— The spin-1/2 Heisenberg XXZ chain and the Lorentz mirror model with loop weight 2  (2608.21306 - Ryan, 21 Aug 2026) in Section 1.1, subsection “The Lorentz mirror model with loop weight 2”