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

TL;DR

This study investigates the zero-temperature critical behavior of the 2D Gaussian random bond Ising model on a square lattice, revealing power-law behaviors in specific heat and density of states through high-precision graph expansion and series analysis.

Contribution

It provides the first detailed analysis of low-temperature criticality and density of states in this model, including an exact high-temperature series and a proof regarding spin flip states.

Findings

Specific heat follows a power law with exponent 1+α at low T

Density of states follows a power law with exponent α at low energies

High-temperature series expanded up to β^{29}

Abstract

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.