Zero-temperature criticality in the Gaussian random bond Ising model on a square lattice

The free energy and the specific heat of the two-dimensional Gaussian random bond Ising model on a square lattice are found with high accuracy using graph expansion method. At low temperatures the specific heat reveals a zero-temperature criticality described by the power law $C\propto T^{1+\alpha}$, with $\alpha= 0.55(8)$. Interpretation of the free energy in terms of independent two-level excitations gives the density of states, that follows a novel power law $\rho(\epsilon)\propto \epsilon^\alpha$ at low energies. An exact high-temperature series for this model up to the term $\beta^{29}$ is found. A proof that the density of one-site spin flip states vanishes at low energy is given.