Duality in finite-dimensional spin glasses

Abstract

We present an analysis leading to a conjecture on the exact location of the multicritical point in the phase diagram of spin glasses in finite dimensions. The conjecture, in satisfactory agreement with a number of numerical results, was previously derived using an ansatz emerging from duality and the replica method. In the present paper we carefully examine the ansatz and reduce it to a hypothesis on analyticity of a function appearing in the duality relation. Thus the problem is now clearer than before from a mathematical point of view: The ansatz, somewhat arbitrarily introduced previously, has now been shown to be closely related to the analyticity of a well-defined function.

12 pages, 3 figures; A reference added; to appear in J. Stat. Phys

References in corpus (12)

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Cited by in corpus (16)

• Locations of multicritical points for spin glasses on regular lattices
• Multicritical points for the spin glass models on hierarchical lattices
• Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice +- J Ising model
• Multicritical Nishimori point in the phase diagram of the +- J Ising model on a square lattice
• Magnetic-glassy multicritical behavior of the three-dimensional +- J Ising model
• Optimal Thresholds for Fracton Codes and Random Spin Models with Subsystem Symmetry
• Analytical evidence for the absence of spin glass transition on self-dual lattices
• Reentrant and Forward Phase Diagrams of the Anisotropic Three-Dimensional Ising Spin Glass
• Tapestry of dualities in decohered quantum error correction codes
• High-precision phase diagram of spin glasses from duality analysis with real-space renormalization and graph polynomials
• Coherent information as a mixed-state topological order parameter of fermions
• Phase Transitions in Nonlinear Filtering
• Multicritical point of spin glasses
• A simple relation between frustration and transition points in diluted spin glasses
• Revisiting Nishimori multicriticality through the lens of information measures
• Error Resilience of Fracton Codes and Near Saturation of Code-Capacity Threshold in Three Dimensions