Strong Randomness Fixed Point in the Dissipative Random Transverse Field Ising Model

TL;DR

This paper investigates the effects of disorder, quantum fluctuations, and dissipation in a random transverse Ising chain, revealing a strong randomness fixed point and the dominance of frozen clusters at large scales, with implications for low-temperature behavior.

Contribution

It introduces a real space renormalization group analysis of the dissipative random transverse Ising model, identifying a strong randomness fixed point and large-scale frozen cluster effects.

Findings

Existence of a large length scale L* where frozen clusters dominate

Presence of a strong disorder fixed point influencing scaling behavior

Finite magnetization and classical behavior in a Griffiths-McCoy region

Abstract

The interplay between disorder, quantum fluctuations and dissipation is studied in the random transverse Ising chain coupled to a dissipative Ohmic bath with a real space renormalization group. A typically very large length scale, L*, is identified above which the physics of frozen clusters dominates. Below L* a strong disorder fixed point determines scaling at a pseudo-critical point. In a Griffiths-McCoy region frozen clusters produce already a finite magnetization resulting in a classical low temperature behavior of the susceptibility and specific heat. These override the confluent singularities that are characterized by a continuously varying exponent z and are visible above a temperature T* ~ L*^{-z}.