The Boundary Conditions Geometry in Lattice-Ising Model

TL;DR

This paper explores how the differential and geometric topologies of lattice systems influence phase transitions, ordering, and spin orientations in the Ising model, revealing topological constraints on physical phenomena.

Contribution

It introduces a topological framework linking lattice geometry and topology to phase transition behavior and spin orientation in the Ising model.

Findings

Differential topology determines the possibility of continuous phase transitions.

Geometric topology influences the system's ability to become ordered.

Ordered systems may not support continuous phase transitions.

Abstract

We found that the differential topology of the lattice-system of Ising model determines whether there can be the continuous phase transition, the geometric topology of the space the lattice-system is embedded in determines whether the system can become ordered. If the system becomes ordered it may not admit the continuous phase transition. The spin-projection orientations are strongly influenced by the geometric topology of the space the lattice-system is embedded in.