Random bond Ising chain in a transverse magnetic field: A finite-size scaling analysis

TL;DR

This paper analyzes the quantum phase transition in a disordered Ising chain under a transverse magnetic field, revealing critical properties similar to a classical layered disordered model through finite-size scaling.

Contribution

It provides a finite-size scaling analysis of the critical behavior of a random bond Ising chain in a transverse field, linking quantum and classical disordered systems.

Findings

Critical exponents match those of the McCoy-Wu model

Magnetization and susceptibility follow conventional scaling

Distribution of order parameter shows nontrivial scaling

Abstract

We investigate the zero-temperature quantum phase transition of the random bond Ising chain in a transverse magnetic field. Its critical properties are identical to those of the McCoy-Wu model, which is a classical Ising model in two dimensions with layered disorder. The latter is studied via Monte Carlo simulations and transfer matrix calculations and the critical exponents are determined with a finite-size scaling analysis. The magnetization and susceptibility obey conventional rather than activated scaling. We observe that the order parameter-- and correlation function--probability distribution show a nontrivial scaling near the critical point which implies a hierarchy of critical exponents associated with the critical behavior of the generalized correlation lengths.