Elementary excitations and the phase transition in the bimodal Ising spin glassmodel

Abstract

We show how the nature of the phase transition in the two-dimensionalbimodal Ising spin glass model can be understood in terms of elementaryexcitations. Although the energy gap with the ground state is expected to be4J in the ferromagneticphase, a gap 2J is in fact found if the finite lattice is wound around a cylinder of odd circumferenceL. This2J gap is really a finite size effect that should not occur in the thermodynamic limit of the ferromagnet.The spatial influence of the frustration must be limited and not wrap around the system ifL is large enough. Inessence, the absence of 2J excitations defines the ferromagnetic phase without recourse to calculating themagnetization or investigating the system response to domain wall defects. This studydirectly investigates the response to temperature. We also estimate the defectconcentration where the phase transition to the spin glass state occurs. The valuepc = 0.1045(11) is in reasonable agreement with the literature.