Quantum Critical Behavior of the Infinite-range Transverse Ising Spin Glass : An Exact Numerical Diagonalization Study
Abstract
We report exact numerical diagonalization results of the infinite-range Ising spin glass in a transverse field
Γ
at zero temperature. Eigenvalues and eigenvectors are determined for various strengths of
Γ
and for system sizes
N≤16
. We obtain the moments of the distribution of the spin-glass order parameter, the spin-glass susceptibility and the mass gap at different values of
Γ
. The disorder averaging is done typically over 1000 configurations. Our finite size scaling analysis indicates a spin glass transition at
Γ
c
≃1.5
. Our estimates for the exponents at the transition are in agreement with those known from other approaches. For the dynamic exponent, we get
z=2.1±0.1
which is in contradiction with a recent estimate (
z=4
). Our cumulant analysis indicates the existence of a replica symmetric spin glass phase for
Γ<
Γ
c
.