# Affine lattice construction of spiral surfaces in classical Heisenberg models

## TL;DR

This paper introduces a method to construct classical Heisenberg spin models with degenerate ground states forming manifolds in reciprocal space, and discusses how fluctuations influence order stabilization.

## Contribution

It provides an explicit construction technique for models with codimension-one manifolds in reciprocal space, advancing understanding of frustration and degeneracy in spin systems.

## Key findings

- Constructs models with line and surface degeneracies in reciprocal space.
- Analyzes the impact of thermal and quantum fluctuations on order stabilization.
- Provides a systematic recipe for designing frustrated spin models.

## Abstract

Frustration in classical spin models can lead to degenerate ground states without long range order. In reciprocal space, these degeneracies appear as manifolds of wave vectors, their dimensionality increasing with the degree of frustration and the robustness of the disordered spin-liquid state. Here, we present a recipe to explicitly construct Heisenberg models on Bravais lattices with codimension-one manifolds, i.e., lines in two-dimensions and surfaces with different Euler characteristics in three-dimensions. Furthermore, we discuss the role of thermal and quantum fluctuations in stabilizing ordered states.