On bimodal size distribution of spin clusters in the onedimensional Ising model

A Ivanytskyi,V Chelnokov,Y Aharonov,S Kabana,L Bravina

doi:10.1051/epjconf/201818203004

A Ivanytskyi, V Chelnokov + Show 3 more

Open Access

https://doi.org/10.1051/epjconf/201818203004

Copy DOI

Abstract

The size distribution of geometrical spin clusters is exactly found for the onedimensional Ising model of finite extent. For the values of lattice constant β above some “critical value” βc the found size distribution demonstrates the non-monotonic behaviour with the peak corresponding to the size of the largest available cluster. In other words, for high values of the lattice constant there are two ways to fill the lattice: either to form a single largest cluster or to create many clusters of small sizes. This feature closely resembles the well-know bimodal size distribution of clusters which is usually interpreted as a robust signal of the first order liquid-gas phase transition in finite systems. It is remarkable that the bimodal size distribution of spin clusters appears in the one-dimensional Ising model of finite size, i.e. in the model which in thermodynamic limit has no phase transition at all.

Highlights

During the last two decades the experimental studies of phase transitions in finite and even in small systems have inspired a high interest to their rigorous theoretical treatment [2? –4]
The growing interest in a bimodality is caused by the widespread belief that it can serve as a robust signal of the first order phase transition in finite systems
Using the exact formulae we showed that for finite size of the lattice the one-dimensional Ising model has a bimodal size distribution of clusters for β > ln 2/2

Summary

Introduction

During the last two decades the experimental studies of phase transitions in finite and even in small systems have inspired a high interest to their rigorous theoretical treatment [2? –4]. In order to demonstrate that this is, the case and that the statistical systems in finite volume can generate the bimodal size distributions, here we analytically calculate the size distribution of geometrical spin clusters of the simplest statistical model which has no phase transition, the one-dimensional Ising model [21]. Another principal purpose of this work is to further develop connections between the spin and cluster models respectively.

Cluster size distribution

Bimodality manifestation

Conclusions and perspectives