Specific heat of the Gaussian random bond Ising model on a square lattice

Details Specific heat of the Gaussian random bond Ising model on a square lattice Specific heat of the Gaussian random bond Ising model on a square lattice

2011-03-31

arxiv.org/abs/1104.0037v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, 3 figures

Scientific paper

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 and analysis of continuation of the high-temperature series. At low temperatures the specific heat follows the power law $C\propto T^{3/2}$, the result confirmed independently by counting many-body states in finite size samples. The interpretation of the free energy in terms of independent droplet excitations gives the density of the two-level states, that follows a novel power law $\rho(\epsilon)\propto \sqrt{\epsilon}$ at low energies.

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