Universality of striped morphologies

TL;DR

This paper introduces a method to predict low-temperature morphologies in spherical and Ising spin models, revealing universal emergence of striped patterns due to energetic preferences influenced by potential properties.

Contribution

It provides an exact determination of ground state length scales for spherical models and explains the universal appearance of striped morphologies in Ising models.

Findings

Ground state length scales are exactly determined for spherical models.

Striped morphologies are energetically favored in Ising models due to discretization effects.

Striped patterns emerge universally as ground states for certain potentials.

Abstract

We present a method for predicting the low-temperature behavior of spherical and Ising spin models with isotropic potentials. For the spherical model the characteristic length scales of the ground states are exactly determined but the morphology is shown to be degenerate with checkerboard patterns, stripes and more complex morphologies having identical energy. For the Ising models we show that the discretization breaks the degeneracy causing striped morphologies to be energetically favored and therefore they arise universally as ground states to potentials whose Hankel transforms have nontrivial minima.