Correlation--function distributions at the Nishimori point of two-dimensional Ising spin glasses

Abstract

The multicritical behavior at the Nishimori point of two-dimensional Ising spin glasses is investigated by using numerical transfer-matrix methods to calculate probability distributions $P(C)$ and associated moments of spin-spin correlation functions $C$ on strips. The angular dependence of the shape of correlation function distributions $P(C)$ provides a stringent test of how well they obey predictions of conformal invariance; and an even symmetry of $(1-C)P(C)$ reflects the consequences of the Ising spin-glass gauge (Nishimori) symmetry. We show that conformal invariance is obeyed in its strictest form, and the associated scaling of the moments of the distribution is examined, in order to assess the validity of a recent conjecture on the exact localization of the Nishimori point. Power law divergences of $P(C)$ are observed near C=1 and C=0, in partial accord with a simple scaling scheme which preserves the gauge symmetry.

Final version to be published in Phys Rev B

References in corpus (4)

• The two-dimensional random-bond Ising model, free fermions and the network model
• Duality and Multicritical Point of Two-Dimensional Spin Glasses
• Symmetry, complexity and multicritical point of the two-dimensional spin glass
• Derivatives and inequalities for order parameters in the Ising spin glass

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• Multicritical Nishimori point in the phase diagram of the +- J Ising model on a square lattice
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• Multicritical point of Ising spin glasses on triangular and honeycomb lattices
• Exact location of the multicritical point for finite-dimensional spin glasses: A conjecture
• On locations and properties of the multicritical point of Gaussian and +/-J Ising spin glasses
• An exact algorithm for spin correlation functions of the two dimensional +/-J Ising spin glass in the ground state
• Finite-size scaling behavior in trapped systems
• Logarithmic corrections to correlation decay in two-dimensional random-bond Ising systems
• Properties of the multicritical point of +/- J Ising spin glasses on the square lattice
• Boundary Criticality at the Nishimori Multicritical Point