A simple relation between frustration and transition points in diluted spin glasses

Abstract

We investigate a possible relation between frustration and phase-transition points in spin glasses. The relation is represented as a condition of the number of frustrated plaquettes in the lattice at phase-transition points at zero temperature and was reported to provide very close points to the phase-transition points for several lattices. Although there has been no proof of the relation, the good correspondence in several lattices suggests the validity of the relation and some important role of frustration in the phase transitions. To examine the relation further, we present a natural extension of the relation to diluted lattices and verify its effectiveness for bond-diluted square lattices. We then confirm that the resulting points are in good agreement with the phase-transition points in a wide range of dilution rate. Our result supports the suggestion from the previous work for non-diluted lattices on the importance of frustration to the phase transition of spin glasses.

arXiv comment6 pages, 4 figures

References in corpus (26)

• Fault-tolerant quantum computation by anyons
• Topological quantum memory
• Mean field theory of hard sphere glasses and jamming
• Fractal free energy landscapes in structural glasses
• Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
• Thresholds for topological codes in the presence of loss
• Nishimori point in the 2D +/- J random-bond Ising model
• Error Correction and Degeneracy in Surface Codes Suffering Loss
• Locations of multicritical points for spin glasses on regular lattices
• Domain-Wall Energies and Magnetization of the Two-Dimensional Random-Bond Ising Model
• Multicritical points for the spin glass models on hierarchical lattices
• Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice +- J Ising model
• Multicritical point of Ising spin glasses on triangular and honeycomb lattices
• Error- and Loss-Tolerances of Surface Codes with General Lattice Structures
• Domain-wall excitations in the two-dimensional Ising spin glass
• Analytical evidence for the absence of spin glass transition on self-dual lattices
• Error threshold estimates for surface code with loss of qubits
• Duality in finite-dimensional spin glasses
• Duality analysis on random planar lattice
• Gauge Theory for Quantum Spin Glasses
• Zero-temperature spinglass-ferromagnetic transition : scaling analysis of the domain-wall energy
• High-precision phase diagram of spin glasses from duality analysis with real-space renormalization and graph polynomials
• Elementary excitations and the phase transition in the bimodal Ising spin glass model
• Duality with real-space renormalization and its application to bond percolation
• Frustration in vicinity of transition point of Ising spin glasses
• An extension of estimation of critical points in ground state for random spin systems