Spontaneous symmetry breaking at any temperature in a local one-dimensional model

We present a one-dimensional classical statistical physics model on an infinite lattice with nearest-neighbor interactions and local state space $\mathbb{Z}^2$, with a ``helical" symmetry group $\mathbb{Z}^2\rtimes \mathbb{Z}$ mixing flavor symmetry with spatial translation. For any $0<β<\infty$, we