Zerotemperature criticality in the Gaussian random bond Ising model on a square lattice
Abstract
The free energy and the specific heat of the twodimensional 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 zerotemperature 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 twolevel excitations gives the density of states, that follows a novel power law $\rho(\epsilon)\propto \epsilon^\alpha$ at low energies. An exact hightemperature series for this model up to the term $\beta^{29}$ is found. A proof that the density of onesite spin flip states vanishes at low energy is given.
 Publication:

arXiv eprints
 Pub Date:
 March 2011
 arXiv:
 arXiv:1104.0037
 Bibcode:
 2011arXiv1104.0037D
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics
 EPrint:
 10 pages, 6 figures