Spin glasses and percolation

Abstract

The description of thermodynamic phase transitions in terms of percolation transitions of suitably defined clusters has a long tradition and boasts a number of important successes, the most prominent ones being in ferromagnetic lattice models. Spin glasses and other frustrated systems are not among them as the clusters of aligned spins usually considered in this context start to percolate in the disordered phase and hence fail to indicate the onset of ordering. In this mini-review we provide an overview of the state of the art in this field, including recent advances, and outline the main open questions in the area.

9 pages, 2 figures, to appear in Front. Phys

References in corpus (16)

• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Resilience of the Internet to random breakdowns
• Critical exponents of the three dimensional diluted Ising model
• A Cluster Monte Carlo Algorithm for 2-Dimensional Spin Glasses
• Lower Critical Dimension of Ising Spin Glasses
• Efficient Cluster Algorithm for Spin Glasses in Any Space Dimension
• The critical behavior of 3D Ising glass models: universality and scaling corrections
• Graphical Representations for Ising Systems in External Fields
• The Percolation Signature of the Spin Glass Transition
• Computational hardness of spin-glass problems with tile-planted solutions
• Cluster Monte Carlo algorithms for diluted spin glasses
• Cluster Percolation in the Two-Dimensional Ising Spin Glass
• Percolation of Fortuin-Kasteleyn clusters for the random-bond Ising model
• The Fortuin-Kasteleyn and Damage Spreading transitions in Random bond Ising lattices
• Geometric clusters in the overlap of the Ising model
• Massively parallel simulations for disordered systems

Cited by in corpus (1)

• Cluster percolation in the three-dimensional $\pm J$ random-bond Ising model