Exact results and critical properties of the Ising model with competing interactions

Abstract

The random Ising model with competing interactions is investigated on the basis of the gauge-invariant formulation of the problem. Exact results for the internal energy, specific heat and gauge-invariant correlation function are derived. The critical exponent alpha is shown to be negative at the phase boundary of the paramagnetic and ferromagnetic phases if the latter exists at fairly low concentration of antiferromagnetic bonds.