Magnetic phase transitions in the Ising model

TL;DR

This paper introduces a novel approach to studying order-disorder phase transitions in the Ising model using new order parameters based on percolation cluster sizes, applicable to systems with arbitrary exchange integral distributions.

Contribution

It proposes new order parameters derived from percolation theory to analyze phase transitions in the Ising model, broadening the understanding of disorder-order processes.

Findings

New order parameters for phase transitions are identified.

Percolation theory methods effectively describe the transition from disorder to order.

Applicable to systems with any distribution of exchange integrals signs.

Abstract

In this paper we consider an approach, which allows researching a processes of order-disorder transition in various systems (with any distribution of the exchange integrals signs) in the frame of Ising model. A new order parameters, which can give a description of a phase transitions, are found. The common definition of these order parameters is the mean value of percolation cluster size. Percolation cluster includes spins with given energy. The transition from absolute disorder to correlated phase could be studied with using of percolation theory methods.