Classical spin liquids from frustrated Ising models in hyperbolic space

TL;DR

This paper explores how geometric frustration in hyperbolic space leads to classical spin liquids, with boundary shape influencing ground state order, through exact degeneracy calculations and Monte Carlo simulations.

Contribution

It provides the first detailed analysis of frustrated Ising models in hyperbolic space, revealing boundary-dependent ground states and demonstrating classical spin liquids in curved geometries.

Findings

Boundary shape controls ground state order

Exact ground-state degeneracy for finite systems

Classical spin liquids emerge from geometric frustration

Abstract

Antiferromagnetic Ising models on frustrated lattices can realize classical spin liquids, with highly degenerate ground states and, possibly, fractionalized excitations and emergent gauge fields. Motivated by the recent interest in many-body system in negatively curved space, we study hyperbolic frustrated Ising models. Specifically, we consider nearest-neighbor Ising models on tesselations with odd-length loops in two-dimensional hyperbolic space. For finite systems with open boundaries we determine the ground-state degeneracy exactly, and we perform extensive finite-temperature Monte-Carlo simulations to obtain thermodynamic data as well as correlation functions. We show that the shape of the boundary, constituting an extensive part of the system, can be used to control low-energy states: Depending on the boundary, we find ordered or disordered ground states. Our results demonstrate how geometric frustration acts in curved space to produce classical spin liquids.