Finite temperature behavior of strongly disordered quantum magnets coupled to a dissipative bath

TL;DR

This paper investigates how dissipation influences the critical behavior of disordered quantum magnets, revealing a crossover from Griffiths-McCoy to classical behavior with Ohmic dissipation and identifying an infinite randomness fixed point for super-Ohmic dissipation.

Contribution

It introduces a strong disorder renormalization group method to analyze finite temperature properties of disordered quantum magnets with dissipation.

Findings

Susceptibility shows crossover from Griffiths-McCoy to Curie behavior with Ohmic dissipation.

Specific heat exhibits Griffiths-McCoy singularities across all temperatures.

Infinite randomness fixed point persists for super-Ohmic dissipation, with analytically determined phase diagram.

Abstract

We study the effect of dissipation on the infinite randomness fixed point and the Griffiths-McCoy singularities of random transverse Ising systems in chains, ladders and in two-dimensions. A strong disorder renormalization group scheme is presented that allows the computation of the finite temperature behavior of the magnetic susceptibility and the spin specific heat. In the case of Ohmic dissipation the susceptibility displays a crossover from Griffiths-McCoy behavior (with a continuously varying dynamical exponent) to classical Curie behavior at some temperature $T^*$. The specific heat displays Griffiths-McCoy singularities over the whole temperature range. For super-Ohmic dissipation we find an infinite randomness fixed point within the same universality class as the transverse Ising system without dissipation. In this case the phase diagram and the parameter dependence of the dynamical exponent in the Griffiths-McCoy phase can be determined analytically.