Relaxational behavior of the infinite-range Ising spin-glass in a transverse field

TL;DR

This paper investigates the zero-temperature quantum transition of an infinite-range Ising spin glass in a transverse field, revealing critical exponents and relaxation dynamics through computational methods.

Contribution

It provides new estimates for critical exponents and characterizes the relaxation behavior of the model at zero temperature.

Findings

Correlation length exponent ν ≈ 1/4

Dynamical exponent z = 4

Energy relaxation follows a t^{-1} decay

Abstract

We study the zero-temperature behavior of the infinite-ranged Ising spin glass in a transverse field. Using spin summation techniques and Monte Carlo methods we characterize the zero-temperature quantum transition. Our results are well compatible with a value $\nu=\frac{1}{4}$ for the correlation length exponent, $z=4$ for the dynamical exponent and an algebraic decay $t^{-1}$ for the imaginary-time correlation function. The zero-temperature relaxation of the energy in the presence of the transverse field shows that the system monotonically reaches the ground state energy due to tunneling processes and displays strong glassy effects.