Universality of the glassy transitions in the two-dimensional +- J Ising model

Abstract

We investigate the zero-temperature glassy transitions in the square-lattice +- J Ising model, with bond distribution $P(J_{xy})=p\delta (J_{xy}-J)+(1-p)\delta (J_{xy}+J)$; p=1 and p=1/2 correspond to the pure Ising model and to the Ising spin glass with symmetric bimodal distribution, respectively. We present finite-temperature Monte Carlo simulations at p=4/5, which is close to the low-temperature paramagnetic-ferromagnetic transition line located at p=0.89, and at p=1/2. Their comparison provides a strong evidence that the glassy critical behavior that occurs for $1-p_0<p<p_0$, $p_0=0.897$, is universal, i.e., independent of p. Moreover, we show that glassy and magnetic modes are not coupled at the multicritical zero-temperature point where the paramagnetic-ferromagnetic transition line and the T=0 glassy transition line meet. On the theoretical side we discuss the validity of finite-size scaling in glassy systems with a zero-temperature transition and a discrete Hamiltonian spectrum. Because of a freezing phenomenon which occurs in a finite volume at sufficiently low temperatures, the standard finite-size scaling limit in terms of $T{L}^{1/\nu }$ does not exist: the renormalization-group invariant quantity $\xi /L$ should be used instead as basic variable.

arXiv comment9 pages, 17 figs

References in corpus (30)

• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Parallel Tempering: Theory, Applications, and New Perspectives
• Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
• A Cluster Monte Carlo Algorithm for 2-Dimensional Spin Glasses
• Low-temperature behavior of two-dimensional Gaussian Ising spin glasses
• Lower Critical Dimension of Ising Spin Glasses
• The critical behavior of three-dimensional Ising spin glass models
• The critical exponents of the two-dimensional Ising spin glass revisited: Exact Ground State Calculations and Monte Carlo Simulations
• Finite-Size Scaling at $\xi /L\gg 1$
• Aspect-Ratio Scaling and The Stiffness Exponent $\theta$ for Ising Spin Glasses
• Duality and Multicritical Point of Two-Dimensional Spin Glasses
• Scalings of domain wall energies in two dimensional Ising spin glasses
• Strong universality and algebraic scaling in two-dimensional Ising spin glasses
• Locations of multicritical points for spin glasses on regular lattices
• Universal dependence on disorder of 2D randomly diluted and random-bond +-J Ising models
• Domain-Wall Energies and Magnetization of the Two-Dimensional Random-Bond Ising Model
• Strong disorder fixed points in the two-dimensional random-bond Ising model
• Correlation length of the two-dimensional Ising spin glass with bimodal interactions
• Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice +- J Ising model
• Critical thermodynamics of the two-dimensional +/-J Ising spin glass
• Multicritical Nishimori point in the phase diagram of the +- J Ising model on a square lattice
• The critical behavior of 3D Ising glass models: universality and scaling corrections
• Effective critical behavior of the two-dimensional Ising spin glass with bimodal interactions
• Ground states of two-dimensional $\pm$J Edwards-Anderson spin glasses
• Correlation Length of the Two-Dimensional Ising Spin Glass with Gaussian Interactions
• Analytical evidence for the absence of spin glass transition on self-dual lattices
• Evidence for universal scaling in the spin-glass phase
• Magnetic and glassy transitions in the square-lattice XY model with random phase shifts
• Entropic Effects in the Very Low Temperature Regime of Diluted Ising Spin Glasses with Discrete Couplings
• Zero-temperature behavior of the random-anisotropy model in the strong-anisotropy limit

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