Absence of jump discontinuity in the magnetization in quasi-one-dimensional random-field Ising models

TL;DR

This paper proves that in certain one-dimensional and quasi-one-dimensional random-field Ising models at zero temperature, the magnetization varies smoothly with the external field, showing no abrupt jumps.

Contribution

It demonstrates the absence of jump discontinuities in magnetization for these models and introduces a stochastic matrix approach to analyze the system's evolution.

Findings

Magnetization is a continuous and differentiable function of the external field.

The system's evolution can be described by a stochastic matrix with a unique eigenvector.

No jump discontinuity occurs in the magnetization for the studied models.

Abstract

We consider the zero-temperature random-field Ising model in the presence of an external field, on ladders and in one dimension with finite range interactions, for unbounded continuous distributions of random fields, and show that there is no jump discontinuity in the magnetizations for any quasi-one dimensional model. We show that the evolution of the system at an external field can be described by a stochastic matrix and the magnetization can be obtained using the eigenvector of the matrix corresponding to the eigenvalue one, which is continuous and differentiable function of the external field.