Ising model: secondary phase transition

TL;DR

This paper proposes a new understanding of phase transitions in the Ising model by incorporating lattice-spin phonons, predicting a Bose-Einstein condensation (BEC) transition and linking it to experimental heat capacity observations.

Contribution

It introduces the concept of lattice-spin phonons causing a BEC phase transition in the Ising model, expanding the theoretical framework beyond traditional spin-wave theory.

Findings

Heat capacity at critical temperature aligns with experiments

Magnons share characteristics with lattice-spin phonons after BEC transition

Energy-level overlap effect observed at ultralow temperatures

Abstract

Lttice-spin phonons are considered, which make the heat capacity at the critical temperature satisfy experimental observations better. There is a BEC phase transition in an Ising model attributable to the lattice-spin phonons. We proved that the spin-wave theory only is available after BEC transition, and the magnons have the same characteristics as the lattice-spin phonons', resulting from quantum effect. Energy-level overlap effect at ultralow temperature is found. A prediction of BEC phase transition in a crystal is put forward as our theory generalization.