3D Spin Glass and 2D Ferromagnetic XY Model: a Comparison

Abstract

We compare the probability distributions and Binder cumulants of the overlap in the 3D Ising spin glass with those of the magnetization in the ferromagnetic 2D XY model. We analyze similarities and differences. Evidence for the existence of a phase transition in the spin glass model is obtained thanks to the crossing of the Binder cumulant. We show that the behavior of the XY model is fully compatible with the Kosterlitz-Thouless scenario. Finite size effects have to be dealt with by using great care in order to discern among two very different physical pictures that can look very similar if analyzed without large attention.

14 pages and 6 figures. Also available at http://chimera.roma1.infn.it/index_papers_complex.html

References in corpus (2)

• About the overlap distribution in mean field spin glass models
• Mean Field Dynamical Exponents in Finite-Dimensional Ising Spin Glass

Cited by in corpus (19)

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• Violation of the Fluctuation Dissipation Theorem in Finite Dimensional Spin Glasses
• Nonequilibrium Critical Dynamics of the 2D XY model
• Critical parameters of the three-dimensional Ising spin glass
• On the Phase Structure of the 3D Edwards Anderson Spin Glass
• Nature of the spin-glass phase at experimental length scales
• Small Window Overlaps Are Effective Probes of Replica Symmetry Breaking in 3D Spin Glasses
• Phase Transition of XY Model in Heptagonal Lattice
• Comment on ``Spin-glass transition of the three-dimensional Heisenberg spin glass''
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• Study of the phase transition in the 3d Ising spin glass from out of equilibrium numerical simulations
• Kosterlitz-Thouless Phase Transition of the ANNNI model in Two Dimensions
• Phase diagram of a three-dimensional dipolar Ising model with textured Ising axes
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