Phase separation on a hyperbolic lattice

TL;DR

This study investigates how phase separation dynamics differ on hyperbolic lattices compared to Euclidean lattices, revealing significantly slower domain growth on hyperbolic geometries through kinetic Monte Carlo simulations.

Contribution

It provides the first numerical comparison of phase separation on hyperbolic versus Euclidean lattices, highlighting unique growth exponents in hyperbolic geometry.

Findings

Power-law domain growth with exponent ~1/3 on Euclidean lattices

Slower domain growth with exponent ~0.13 on hyperbolic lattices

Introduction to non-Euclidean lattices and their Euclidean mapping

Abstract

We report a preliminary numerical study by kinetic Monte Carlo simulation of the dynamics of phase separation following a quench from high to low temperature in a system with a single, conserved, scalar order parameter (a kinetic Ising ferromagnet) confined to a hyperbolic lattice. The results are compared with simulations of the same system on two different, Euclidean lattices, in which cases we observe power-law domain growth with an exponent near the theoretically known value of 1/3. For the hyperbolic lattice we observe much slower domain growth, consistent to within our current accuracy with power-law growth with a much smaller exponent near 0.13. The paper also includes a brief introduction to non-Euclidean lattices and their mapping to the Euclidean plane.