Zero- and low-temperature behavior of the two-dimensional ±J Ising spin glass

Scaling arguments and precise simulations are used to study the square lattice ±J Ising spin glass, a prototypical model for glassy systems. Droplet theory explains, and our numerical results show, entropically stabilized long-range spin-glass order at zero temperature, which resembles the energetic stabilization of long-range order in higher-dimensional models at finite temperature. At low temperature, a temperature-dependent crossover length scale is used to predict the power-law dependence on temperature of the heat capacity and clarify the importance of disorder distributions.     

Spin-correlation function of the fully frustrated Ising model and ± J Ising spin glass on the square lattice

In this work we study the correlation function of the ground state of two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as correlation function. We estimate the exponent of spin correlation function for fully frustrated model and spin glass. In this paper an overview of the latest results on the spin correlation function is presented.     

Spin-correlation function of the fully frustrated Ising model and ±J Ising spin glass on a square lattice

In this work we study the correlation function of the ground state of a two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as the correlation function. We estimate the exponent of spin correlation function for the fully frustrated model and spin glass. In this paper an overview of the latest results on the spin correlation function is presented.     

Geometric localization of the threshold in two-dimensional Ising ±J spin glasses forT=0

Following an approach of Toulouse, ground states in random 2D Ising ±J spin glasses (without external magnetic field), on square lattices, and with concentrations 0p0.5 of antiferromagnetic bonds are studied by means of minimal matchings of frustrated plaquettes. Lete(p) be the ground-state energy per spin in the thermodynamic limit. Then the well-known equatione(p)=–2+(p)f(p) holds, wheref(p) is the concentration of frustrated plaquettes and(p) is the average connection length between paired frustrated plaquettes in minimal matchings. Introducing (p) as the probability that a frustrated plaquette is matched to another frustrated plaquette by a connection of length (in a minimal matching), the average length(p) can be rewritten asgl(p)=(p). The study of(p) and its components (p) leads to an intervalp ^*pp ₂ (p ^*0.121±0.008,p ₂0.161±0.008) where the threshold between ferromagnet and paramagnet forT=0 lies. Analyzing a similar so-called adjoined average lengthl(p) admits further insight.     

Exact ground states of two-dimensional ±J Ising spin glasses

In this paper we study the problem of finding an exact ground state of a two-dimensional ±J Ising spin glass on a square lattice with nearest neighbor interactions and periodic boundary conditions when there is a concentrationp of negative bonds, withp ranging between 0.1 and 0.9. With our exact algorithm we can determine ground states of grids of sizes up to 50×50 in a moderate amount of computation time (up to 1 hr each) for several values ofp. For the ground-state energy of an infinite spin-glass system withp=0.5 we estimateE _0.5 =–1.4015±0.0008. We report on extensive computational tests based on more than 22,000 experiments.     

Ultrasonic absorption with infrared divergence in cluster spin glass

The infrared divergence response theory is applied toreorientational relaxation process of magnetic clusters in cluster spinglass(CoF_2)_(0.5)(BaF_2)_/(0.2)(NaPO_3)_(0.3)to study the behaviour of low temper-ature ultrasonic absorption in this system.Our calculation results showedthat the reorientational relaxation process makes the main contributions tothe magnetic part of the ultrasonic absorption for T<4.0K;as forT>4.0K,the contributions of the internal process inside the clustersmust be considered.     

Strong-Disorder Paramagnetic-Ferromagnetic Fixed Point in the Square-Lattice ±J Ising Model

We consider the random-bond ±J Ising model on a square lattice as a function of the temperature T and of the disorder parameter p (p=1 corresponds to the pure Ising model). We investigate the critical behavior along the paramagnetic-ferromagnetic transition line at low temperatures, below the temperature of the multicritical Nishimori point at T ^*=0.9527(1), p ^*=0.89083(3). We present finite-size scaling analyses of Monte Carlo results at two temperature values, T≈0.645 and T=0.5. The results show that the paramagnetic-ferromagnetic transition line is reentrant for T<T ^*, that the transitions are continuous and controlled by a strong-disorder fixed point with critical exponents ν=1.50(4), η=0.128(8), and β=0.095(5). This fixed point is definitely different from the Ising fixed point controlling the paramagnetic-ferromagnetic transitions for T>T ^*. Our results for the critical exponents are consistent with the hyperscaling relation 2β/ν?η=d?2=0.     

On the ground-state threshold in random two-dimensional Ising ±J models

For square, triangular, and for hexagonal lattices there is numerical and theoretical support that the ground-state thresholdp _c between ferro- and paramagnetism in random 2D Ising ±J models, withp as the concentration of antiferromagnetic bonds, is identical top ^*which is characterized by minimal matching properties of frustrated plaquettes. From square lattices of size 100×100 we have got p_c,sq<0.117 by simulations which produced average groundstate magnetizations per spin by means of exact minimal matchings. Moreover, from the squareL×L-lattices treated (L = 10, 20, 50, 100) we obtained the estimatep _c,sq 0.1 which is in agreement with the Grinstein estimatep _c,sq 0.099 andp _c,sq 0.105 by Freund and Grassberger.     

Two-dimensional mixed spin Ising models with bond dilution and random ±J interactions

Using the finite cluster approximation we study a mixed spin model (spins =1/2 andS=1) on a square lattice with nearest-neighbour and crystal field interactions. The nearest-neighbour couplingsK _ij are assumed to be independent random variables with distribution,P(K _ij )=p(K _ij –K)+(1–p)(K _ij –K), whereK>0. We investigate the cases =0 and =–1 corresponding to bond dilution and to random ±J interactions, respectively. In certain ranges ofp the phase diagrams exhibit tricritical behaviour and reentrance.Supported by the agreement of cooperation between the DFG and the CNR-MarocOn leave from Faculté des Sciences I, Université Hassan II, Casablanca, Morocco; and Laboratoire de Magnétisme Université de Rabat, Morocco     

The ground-state energy of the ±J sping glass. A comparison of various biologically motivated algorithms

We compare various evlutionary strategies to determine the ground-state energy of the ±J spin glass. We show that the choice of different evolution laws is less important than a suitable treatment of the free spins of the system At least one combination of these strategies does not give the correct results, but the ground states of the other different strategies coincide. Therefore we are able to extrapolate the infinit-size ground-state energy for the square lattice to –1.401±0.0015 and for the simple cubic lattice to –1.786±0.004.     

Spin dynamics in the spin glass phase of Y(Mn1−xAlx)2

Zero field SR has been used to probe spin dynamics in the concentrated spin glass Y(Mn_0.9Al_0.1)₂. The spectra follow a stretched exponential form, G_z(t)=exp(–(t)), with reaching 1/3 as the freezing temperature, T_g=60K, is approached. The evolution of G_z(t) with temperature is suggestive of the behaviour of the spin correlation function found by Ogielski in Monte Carlo simulations of the dynamics of the Ising spin glass model. The SR results are correlated with results previously obtained by inelastic neutron scattering.     

Challenges in uncovering the origin of the proton's spin

One of the most fascinating challenges facing modern strong interaction physics is to understand the origin of the spin of the nucleon in terms of the spin and orbital angular momentum of the quarks and gluons.We review recent progress on this problem as well as some of the uncertainties associated with state of the art lattice QCD simulations.In particular,we explain the importance of the corrections associated with chiral extrapolation and finite volume corrections,especially for the term B（0） extracted from the appropriate low moment of the deeply virtual Compton scattering amplitude.     

CP violation and strong phases from penguins in B±→PP and B±→VP decays

We calculate direct CP-violating rate asymmetries in chargedB→PP andB→VP decays arising from the interference of amplitudes with different strong and CKM phases. The perturbative strong phases develop at order α _s from absorptive parts of one-loop matrix elements of the next-to-leading logarithm corrected effective Hamiltonian. CPT constraints are maintained. Based on this model, we find that partial rate asymmetries between charge conjugateB ^± decays can be as high as 20% for certain channels with branching ratios in the 10^?6 range. Because the $c\bar c$ threshold lies so close to the physical momentum scale, the asymmetries depend sensitively on the model assumptions used to evaluate the imaginary parts of the matrix elements, in particular, on the internal momentum transfer. The charge asymmetries of partial rates would provide unambiguous evidence for direct CP violation.     

Mössbauer studies of CdCr2xIn2−2xS4:57Fe solid solutions: Reentrant and spin glass like properties

Mössbauer spectroscopy has been performed in CdCr_2xIn_2–2xS₄ spinel solid solutions (0.7x0.95). For x>0.85, reentrant properties are observed: For Tc, finite clusters occurs, decoupled of the ferromagnetic matrix; at low temperature, the ferromagnetic order seems to vanish and a spin glass state occurs. For x0.85, a spin glass state is observed and the properties are coherent rather with a phase transition.On leave of Tata Inst., Bombay 400005 INDIA     

Interaction between phases in the liquid–gas system

This work analyzes the equilibrium between a liquid and a gas over this liquid separated by an interface. Various gas forms exist inside the liquid: dissolved gas molecules attached to solvent molecules, free gas molecules, and gaseous bubbles. Thermodynamic equilibrium is maintained between two phases; the first phase is the liquid containing dissolved and free molecules, and the second phase is the gas over the liquid and bubbles inside it. Kinetics of gas transition between the internal and external gas proceeds through bubbles and includes the processes of bubbles floating up and bubble growth as a result of association due to the Smoluchowski mechanism. Evolution of a gas in the liquid is considered using the example of oxygen in water, and numerical parameters of this system are given. In the regime under consideration for an oxygen–water system, transport of oxygen into the surrounding air proceeds through micron-size bubbles with lifetimes of hours. This regime is realized if the total number of oxygen molecules in water is small compared with the numbers of solvated and free molecules in the liquid.     

Measurements of the mid-rapidity parity violating spin asymmetries for W ± bosons at PHENIX

The parity violating W ^± single spin asymmetry, in longitudinally polarized p + p collisions, can give us a clean way to access the $\Delta \bar u$ and $\Delta \bar d$ polarized parton distribution functions. The current status of the analysis of the 2011 data set and future prospects will be presented.