Crossovers in the two-dimensional Ising spin glass with ferromagnetic next-nearest-neighbour interactions (original) (raw)

Critical behavior of the three-dimensional Ising spin glass

Physical Review B, 2000

We have simulated, using parallel tempering, the three dimensional Ising spin glass model with binary couplings in a helicoidal geometry. The largest lattice (L=20) has been studied using a dedicated computer (the SUE machine). We have obtained, measuring the correlation length in the critical region, a strong evidence for a second-order finite temperature phase transition ruling out other possible scenarios like a Kosterlitz-Thouless phase transition. Precise values for the nu\nunu and eta\etaeta critical exponents are also presented.

Numerical Study of Competing Spin-Glass and Ferromagnetic Order

Physical Review B - PHYS REV B, 1997

Two and three dimensional random Ising models with a Gaussian distribution of couplings with variance J and non-vanishing mean value J0 are studied using the zero-temperature domain-wall renormalization group (DWRG). The DWRG trajectories in the (J_0,J) plane after rescaling can be collapsed on two curves: one for J_0/J > rc and other for J_0/J < r_c. In the first case the DWRG flows are toward the ferromagnetic fixed point both in two and three dimensions while in the second case flows are towards a paramagnetic fixed point and spin-glass fixed point in two and three dimensions respectively. No evidence for an extra phase is found. Click here for the full text of the paper.

Ground-state magnetization of the Ising spin glass: A recursive numerical method and Chen-Ma scaling

Physical review, 2018

The ground-state properties of quasi-one-dimensional (Q1D) Ising spin glass are investigated using an exact numerical approach and analytical arguments. A set of coupled recursive equations for the ground-state energy are introduced and solved numerically. For various types of coupling distribution, we obtain accurate results for magnetization, particularly in the presence of a weak external magnetic field. We show that in the weak magnetic field limit, similar to the 1D model, magnetization exhibits a singular power-law behavior with divergent susceptibility. Remarkably, the spectrum of magnetic exponents is markedly different from that of the 1D system even in the case of two coupled chains. The magnetic exponent makes a crossover from being dependent on the distribution function to a constant value independent of distribution. We provide an analytic theory for these observations by extending the Chen-Ma argument to the Q1D case. We derive an analytical formula for the exponent which is in perfect agreement with the numerical results.

On the 3D Ising spin glass

Journal of Physics A-mathematical and General, 1994

We study the 3d Ising spin glass with ±1 couplings. We introduce a modified local action. We use finite size scaling techniques and very large lattice simulations. We find that our data are compatible both with a finite T transition and with a T = 0 singularity of an unusual type.

Behavior of Ising Spin Glasses in a Magnetic Field

Physical Review Letters, 2008

We study the existence of a spin-glass phase in a field using Monte Carlo simulations performed along a nontrivial path in the field-temperature plane that must cross any putative de Almeida-Thouless instability line. The method is first tested on the Ising spin glass on a Bethe lattice where the instability line separating the spin glass from the paramagnetic state is also computed analytically. While the instability line is reproduced by our simulations on the mean-field Bethe lattice, no such instability line can be found numerically for the short-range three-dimensional model.

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

2009

The spatially uniaxially anisotropic d=3 Ising spin glass is solved exactly on a hierarchical lattice.[1] Five different ordered phases, namely ferromagnetic, columnar, layered, antiferromagnetic, and spin-glass phases, are found in the global phase diagram. The spin-glass phase is more extensive when randomness is introduced within the planes than when it is introduced in lines along one direction. Phase diagram cross-sections, with no Nishimori symmetry, with Nishimori symmetry lines, or entirely imbedded into Nishimori symmetry, are studied. The boundary between the ferromagnetic and spin-glass phases can be either reentrant or forward, that is either receding from or penetrating into the spin-glass phase, as temperature is lowered. However, this boundary is always reentrant when the multicritical point terminating it is on the Nishimori symmetry line. [1] C. G"uven, A.N. Berker, M. Hinczewski, and H. Nishimori, Phys. Rev. E 77, 061110 (2008).

Phase Transition Behaviour of Ising Spin Glass on the FCC Lattice

Communications in Physics, 2013

In this work, we study the nature of phase transition in a face centered cubic (FCC) antiferromagnet with Ising spins. The spin-glass character depends on the concentration \(p\) of ferromagnetic bonds randomly generated into the system. We introduce a new quantity \(M_Q\) combined by the Edwards-Anderson order parameter \(Q\) and the standard magnetization \(M\). Note that, it is impossible to obtain the susceptibility defined by the variance of \(Q\) or \(M\), but we can do that for \(M_Q\). Using the standard Monte-Carlo and powerful Wang-Landau flat-histogram methods, we carry out in this work intensive simulations with many value of ppp. We show that the first-order transition has been destroyed with a tiny amount of ferromagnetic bond \(p\sim 0.01\). With increasing \(p\), the antiferromagnetic phase changes into a spin glass, and then to ferromagnetic phase.

Ground-state properties of the three-dimensional Ising spin glass

Physical Review B, 1994

We study zero-temperature properties of the 3d Edwards-Anderson Ising spin glass on finite lattices up to size 12 3. Using multicanonical sampling we generate large numbers of groundstate configurations in thermal equilibrium. Finite size scaling with a zerotemperature scaling exponent y = 0.74 ± 0.12 describes the data well. Alternatively, a descriptions in terms of Parisi mean field behaviour is still possible. The two scenarios give significantly different predictions on lattices of size ≥ 12 3 .

Two-Dimensional Ising Spin Glasses with Nonzero Ordering Temperatures

Physical Review Letters, 1996

We demonstrate numerically that for Ising spins on square lattices with ferromagnetic second neighbour interactions and random near neighbour interactions, two dimensional Ising spin glass order with a non-zero freezing temperature can occur. We compare some of the physical properties of these spin glasses with those of standard spin glasses in higher dimensions.