Elementary excitations and the phase transition in the bimodal Ising spin glass model

Abstract

We show how the nature of the the phase transition in the two-dimensional bimodal Ising spin glass model can be understood in terms of elementary excitations. Although the energy gap with the ground state is expected to be 4J in the ferromagnetic phase, a gap 2J is in fact found if the finite lattice is wound around a cylinder of odd circumference $L$. This 2J 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 if $L$ is large enough. In essence, the absence of 2J excitations defines the ferromagnetic phase without recourse to calculating magnetisation or investigating the system response to domain wall defects. This study directly investigates the response to temperature. We also estimate the defect concentration where the phase transition to the spin glass glass state occurs. The value $p_c=0.1045(11)$ is in reasonable agreement with the literature.

7 pages, 11 figures

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Cited by in corpus (6)

• Domain-wall excitations in the two-dimensional Ising spin glass
• High-precision phase diagram of spin glasses from duality analysis with real-space renormalization and graph polynomials
• Spin Glass in the Bond-Diluted J1-J2 Ising Model on the Square Lattice
• Frustration in vicinity of transition point of Ising spin glasses
• A simple relation between frustration and transition points in diluted spin glasses
• Analytical estimates of the locations of phase transition points in the ground state for the bimodal Ising spin glass model in two dimensions