Hierarchical freezing in a lattice model

TL;DR

This paper investigates a 2D lattice model with complex phase transitions during slow cooling, revealing hierarchical ordering of sublattices and glass-like states under rapid quenching.

Contribution

It introduces a detailed analysis of hierarchical freezing and phase transitions in a limit-periodic lattice model during temperature quenches.

Findings

Multiple phase transitions occur during slow cooling.

Sublattices with larger lattice constants order sequentially.

Rapid quenching leads to glass-like states due to kinetic barriers.

Abstract

A certain two-dimensional lattice model with nearest and next-nearest neighbor interactions is known to have a limit-periodic ground state. We show that during a slow quench from the high temperature, disordered phase, the ground state emerges through an infinite sequence of phase transitions. We define appropriate order parameters and show that the transitions are related by renormalizations of the temperature scale. As the temperature is decreased, sublattices with increasingly large lattice constants become ordered. A rapid quench results in glass-like state due to kinetic barriers created by simultaneous freezing on sublattices with different lattice constants.