Polymerization in a Ferromagnetic Spin Model with Threshold

TL;DR

This paper introduces a novel ferromagnetic spin model with threshold-dependent interactions, revealing a low-temperature phase characterized by alternating polymers of parallel spins, through mapping to the eight vertex model.

Contribution

It proposes a new type of ferromagnetic interaction based on a threshold, extending traditional spin models and providing insights into phase structures.

Findings

Evidence of a low-temperature phase with alternating spin polymers

Mapping onto the eight vertex model elucidates phase behavior

Threshold-dependent interactions influence spin configurations

Abstract

We propose a spin model with a new kind of ferromagnetic interaction, which may be called {\it ferromagnetic coupling with threshold}. In this model the contribute of a given spin to the total energy has only two possible values and depends on the number of parallel spins among its nearest and next to the nearest neighbors. By mapping the model onto the Ising version of the isotropic eight vertex model, we obtain some evidence of a low temperature phase made of alternate parallel pluses and minuses polymers.