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 (2)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• Multicritical Point Relations in Three Dual Pairs of Hierarchical-Lattice Ising Spin-Glasses

Cited by in corpus (6)

• 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
• Reentrant and Forward Phase Diagrams of the Anisotropic Three-Dimensional Ising Spin Glass