Cluster-Spin Gaussian Model for Lattice-Ising Models

TL;DR

This paper introduces a cluster-spin Gaussian model that simplifies and accurately calculates critical points in lattice-Ising models by analyzing topological properties and fractal dimensions of finite clusters.

Contribution

It presents a novel Gaussian model based on cluster fractal dimensions to determine critical points without conventional methods.

Findings

Accurate calculation of critical points for three lattice systems.

Simplified method reduces computational complexity.

Discussion of multiple cluster types at critical temperature.

Abstract

In this paper we lay special stress on analyzing the topological properties of the lattice systems and try to ovoid the conventional ways to calculate the critical points. Only those clusters with finite sizes can execute the self similar transformations of infinite hierarchies. Each ordered cluster has fractal dimension, their minimum relates to the edge fixed point, which accords with the transformations fixed point relating to a critical point. There are two classes of systems and clusters by their connectivity. Using mathematic mapping method we set up cluster-spin Gaussian model solved accurately. There are single state and -fold coupling state in a reducible cluster, each of which corresponds to a subsystem described by a Gaussian model. By the minimal fractal dimension a final expression of the critical points is obtained. The critical points of three lattice systems are calculated, our method makes the calculations very simplified and highly accurate. A possibility of existence of different clusters at the critical temperature is discussed.