On bimodal size distribution of spin clusters in the one dimensional Ising model

TL;DR

This paper derives the exact size distribution of spin clusters in a finite one-dimensional Ising model, revealing a bimodal distribution at high lattice constants, which resembles phase transition signals despite the absence of a phase transition in the infinite limit.

Contribution

It provides an exact analytical expression for the cluster size distribution in the finite 1D Ising model and uncovers bimodal behavior linked to finite-size effects.

Findings

Bimodal size distribution appears above a critical lattice constant.

Large clusters or many small clusters dominate at high lattice constants.

Bimodality mimics signals of phase transitions in finite systems.

Abstract

The size distribution of geometrical spin clusters is exactly found for the one dimensional Ising model of finite extent. For the values of lattice constant $\beta$ above some "critical value" $\beta_c$ the found size distribution demonstrates the non-monotonic behavior with the peak corresponding to the size of largest available cluster. In other words, at high values of 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.