We study the zero-temperature behaviour of the infinite-ranged Ising spin glass in a transverse field. Using spin summation and Monte Carlo methods we characterize the zero-temperature quantum transition. Our results are well compatible with a value for the correlation length exponent, z=4 for the dynamical exponent and an algebraic decay for the imaginary-time correlation function. The zero-temperature Monte Carlo relaxation of the energy in the presence of the transverse field shows that the system monotonically reaches the ground-state energy due to quantum fluctuations and displays glassy effects due to the strong anisotropy in the effective Hamiltonian.
We perform Monte Carlo simulations of large two-dimensional Gaussian Ising spin glasses down to very low temperatures $\ensuremath{\beta}=1∕T=50$. Equilibration is ensured by using a cluster algorithm including Monte Carlo moves consisting of flipping fundamental excitations. We study the thermodynamic behavior using the Binder cumulant, the spin-glass susceptibility, the distribution of overlaps, the overlap with the ground state, and the specific heat. We confirm that
Tc=0. All results are compatible with an algebraic divergence of the correlation length with an exponent $\ensuremath{\nu}$. We find $\ensuremath{-}1∕\ensuremath{\nu}=\ensuremath{-}0.295(40)$, which is compatible with the value for the domain-wall and droplet exponent $\ensuremath{\theta}\ensuremath{\approx}\ensuremath{-}0.29$ found previously in ground-state studies. Hence the thermodynamic behavior of this model seems to be governed by one single exponent.