Static properties of 2D spin-ice as a sixteen-vertex model

Abstract

We present a thorough study of the static properties of 2D models of spin-ice type on the square lattice or, in other words, the sixteen-vertex model. We use extensive Monte Carlo simulations to determine the phase diagram and critical properties of the finite dimensional system. We put forward a suitable mean-field approximation, by defining the model on carefully chosen trees. We employ the cavity (Bethe-Peierls) method to derive self-consistent equations, the fixed points of which yield the equilibrium properties of the model on the tree-like graph. We compare mean-field and finite dimensional results. We discuss our findings in the context of experiments in artificial two dimensional spin ice.

arXiv comment65 pages

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Cited by in corpus (12)

• Continuous magnetic phase transition in artificial square ice
• Thermal phase transitions in Artificial Spin-Ice
• Quantitative and Interpretable Order Parameters for Phase Transitions from Persistent Homology
• Field-tuned order by disorder in Ising frustrated magnets with antiferromagnetic interactions
• Artificial spin ice and vertex models
• Defects dynamics following thermal quenches in square spin-ice
• Reentrance of disorder in the anisotropic shuriken Ising model
• The 16-vertex model and its even and odd 8-vertex subcases on the square lattice
• Equilibrium Field Theory of Magnetic Monopoles in Degenerate Square Spin Ice: Correlations, Entropic Interactions, and Charge Screening Regimes
• Mean-field phase diagram and spin glass phase of the dipolar Kagome Ising antiferromagnet
• Experimental Measures of Topological Sector Fluctuations in the F-Model
• Pinning-depinning transitions in two classes of discrete elastic-string models in (2+1)-dimensions