Searcharxiv⌕ Search

arXiv subjects

I. A. Campbell

Publications and source records attributed to I. A. Campbell.

At least 55 records · Page 3Linked to original sources
arXiv2005

Ordering temperatures of Ising Spin Glasses

Exploiting an approach due to Singh and Fisher I show that in the high dimension limit the ordering temperature of near neighbour Ising Spin Glasses drops linearly with the kurtosis of the interaction distribution, in excellent agreement with accurate high temperature series data of Daboul, Chang and Aharony. At lower dimensions the linear relation no longer applies strictly but the kurtosis can still be taken to be an appropriate parameter for ranking different systems. I also compare the series estimates with simulation and Migdal-Kadanoff estimates where these are available.

cond-mat.dis-nn↗
arXiv2005

The Anomalous Hall effect in re-entrant AuFe alloys and the real space Berry phase

The Hall effect has been studied in a series of AuFe samples in the re-entrant concentration range, as well as in the spin glass range. The data demonstrate that the degree of canting of the local spins strongly modifies the anomalous Hall effect, in agreement with theoretical predictions associating canting, chirality and a real space Berry phase. The canonical parametrization of the Hall signal for magnetic conductors becomes inappropriate when local spins are canted.

cond-mat.dis-nn↗
arXiv2004

Energy size effects of two-dimensional Ising spin glasses

We analyze exact ground-state energies of two-dimensional Ising spin glasses with either Gaussian or bimodal nearest-neighbor interactions for large system sizes and for three types of boundary conditions: free on both axes, periodic on both axes, and free on one axis and periodic on the other. We find accurate values for bulk-, edge-, and corner-site energies. Fits for the system with Gaussian bonds are excellent for all types of boundary conditions over the whole range of system sizes. In particular, the leading behavior for non-free boundary conditions is governed by the stiffness exponent ~ -0.28 describing the scaling of domain-wall and droplet excitations. For the system with a bimodal distribution of bonds the fit is good for free boundary conditions but worse for other geometries, particularly for periodic-free boundary conditions where there appear to be unorthodox corrections to scaling up to large sizes. Finally, by introducing hard bonds we test explicitly for the Gaussian case the relationship between domain walls and the standard scaling behavior.

cond-mat.dis-nn↗
arXiv2004

Critical properties of the three- and four-dimensional gauge glass

The gauge glass in dimensions 3 and 4 is studied using a variety of numerical methods, in order to obtain accurate and reliable values for the critical parameters. Detailed comparisons are made of the sensitivity of the different techniques to corrections to finite-size scaling, which are generally the major source of systematic error in such measurements. For completeness we also present results in two dimensions. The variation of the critical exponents with space dimension is compared to results in Ising spin glasses.

cond-mat.dis-nn↗
arXiv2003

Chiral susceptibility in canonical spin glass and reentrant alloys from Hall effect measurements

The extraordinary Hall effect coefficients $R_s(T)$ of the canonical spin glass alloys ${\bf Au}Fe 8 at%$ and ${\bf Au}Mn 8 at%$ and of an archetype reentrant system ${\bf Au}Fe 18 at%$ were measured as functions of temperature. The data show a critical cusp-like term superimposed on a smooth background for the spin glasses, and change of sign with temperature for the reentrant. The results can be interpreted consistently by invoking a chiral Hall effect contribution as proposed by Kawamura.

cond-mat.dis-nn↗
arXiv2003

Size dependence of the internal energy in Ising and vector spin glasses

We study numerically the scaling correction to the internal energy per spin as a function of system size and temperature in a variety of Ising and vector spin glasses. From a standard scaling analysis we estimate the effective size correction exponent x at each temperature. For each system with a finite ordering temperature, as temperature is increased from zero, x initially decreases regularly until it goes through a minimum at a temperature close to the critical temperature, and then increases strongly. The behavior of the exponent x at and below the critical temperature is more complex than suggested by the model for the size correction that relates x to the domain-wall stiffness exponent.

cond-mat.dis-nn↗
arXiv2003

Dynamic scaling in spin glasses

We present new Neutron Spin Echo (NSE) results and a revisited analysis of historical data on spin glasses, which reveal a pure power-law time decay of the spin autocorrelation function $s(Q,t) = S(Q,t)/S(Q)$ at the glass temperature $T_g$, each power law exponent being in excellent agreement with that calculated from dynamic and static critical exponents deduced from macroscopic susceptibility measurements made on a quite different time scale. It is the first time that this scaling relation involving exponents of different physical quantities determined by completely independent experimental methods is stringently verified experimentally in a spin glass. As spin glasses are a subgroup of the vast family of glassy systems also comprising structural glasses, other non-crystalline systems living matter the observed strict critical scaling behaviour is important. Above the phase transition the strikingly non-exponential relaxation, best fitted by the Ogielski (power-law times stretched exponential) function, appears as an intrinsic, homogeneous feature of spin glasses.

cond-mat.dis-nn↗
arXiv2002

Ordering in Heisenberg Spin Glasses

For five different Heisenberg spin glass systems, torque experiments were performed in applied magnetic fields up to $4 T$. The Dzyaloshinski-Moriya random anisotropy strengths, the in-field torque onset temperatures, and the torque relaxation were measured. Critical exponents were estimated independently using a standard protocol. The data are strong evidence for a true spin glass ordered state which survives under high applied magnetic fields; they can be interpreted consistently in terms of a chiral ordering model with replica symmetry breaking as proposed by Kawamura and coworkers.

cond-mat.dis-nn↗
arXiv2002

The ordering temperature and critical exponents of the binomial Ising spin glass in dimension three

We compare numerical estimates from different sources for the ordering temperature $T_g$ and the critical exponents of the Ising spin glass in dimension three with binomial ($\pm J$) interactions. Corrections to finite size scaling turn out to be important especially for parameters such as the Binder cumulant. For non-equilibrium parameters it is easier to approach the large size limit and to allow for corrections to scaling. Relying principally on such data, a crossing point defines the freezing temperature $T_g$; the possibility that the ordering temperature is zero can definitively be excluded. We estimate an ordering temperature $T_g = 1.195(15)$, with associated estimates of the critical exponents for which corrections to finite size scaling are well under control. Among the parameters evaluated is the leading dynamic correction to scaling exponent $w$.

cond-mat.dis-nn↗
arXiv2001

Ising Spin Glasses : interaction distribution dependence of the critical exponents

Continuous phase transitions are catalogued into universality classes, families of systems having identical values of all the exponents governing the critical behaviour of their different physical properties. Numerical simulations have been carried out on Ising Spin Glasses in dimension three, using a technique where corrections to finite size scaling can be controled. The data show that the critical exponents vary strongly as a function of the kurtosis of the interaction distribution, a parameter which from the standard point of view should not be pertinent. This observation implies that for spin glasses the renormalization group analysis should not be approached in a the same way as in the case of canonical second order transitions; a much richer structure of universality classes would appear to exist for spin glasses.

cond-mat.dis-nn↗
arXiv2000

Ordered phase in the two-dimensional randomly coupled ferromagnet

True ground states are evaluated for a 2d Ising model with random near neighbor interactions and ferromagnetic second neighbor interactions (the Randomly Coupled Ferromagnet). The spin glass stiffness exponent is positive when the absolute value of the random interaction is weaker than the ferromagnetic interaction. This result demonstrates that in this parameter domain the spin glass like ordering temperature is non-zero for these systems, in strong contrast to the 2d Edwards-Anderson spin glass.

cond-mat.dis-nn↗
arXiv2000

Stretched Exponential Relaxation on the Hypercube and the Glass Transition

We study random walks on the dilute hypercube using an exact enumeration Master equation technique, which is much more efficient than Monte Carlo methods for this problem. For each dilution $p$ the form of the relaxation of the memory function $q(t)$ can be accurately parametrized by a stretched exponential $q(t)=\exp(-(t/τ)^β)$ over several orders of magnitude in $q(t)$. As the critical dilution for percolation $p_c$ is approached, the time constant $τ(p)$ tends to diverge and the stretching exponent $β(p)$ drops towards 1/3. As the same pattern of relaxation is observed in wide class of glass formers, the fractal like morphology of the giant cluster in the dilute hypercube is a good representation of the coarse grained phase space in these systems. For these glass formers the glass transition can be pictured as a percolation transition in phase space.

cond-mat.dis-nn↗
arXiv1999

Ordering in a spin glass under applied magnetic field

Torque, torque relaxation, and magnetization measurements on a AuFe spin glass sample are reported. The experiments carried out up to 7 T show a transverse irreversibility line in the (H,T) plane up to high applied fields, and a distinct strong longitudinal irreversibility line at lower fields. The data demonstrate for that this type of sample, a Heisenberg spin glass with moderately strong anisotropy, the spin glass ordered state survives under high applied fields in contrast to predictions of certain "droplet" type scaling models. The overall phase diagram closely ressembles those of mean field or chiral models, which both have replica symmetry breaking transitions.

cond-mat.dis-nn↗
arXiv1998

The Spin Glass Transition : Exponents and Dynamics

Numerical simulations on Ising Spin Glasses show that spin glass transitions do not obey the usual universality rules which hold at canonical second order transitions. On the other hand the dynamics at the approach to the transition appear to take up a universal form for all spin glasses. The implications for the fundamental physics of transitions in complex systems are addressed.

cond-mat.dis-nn↗
arXiv1997

Critical exponents in Ising spin glasses

We determine accurate values of ordering temperatures and critical exponents for Ising Spin Glass transitions in dimension 4, using a combination of finite size scaling and non-equilibrium scaling techniques. We find that the exponents $η$ and $z$ vary with the form of the interaction distribution, indicating non-universality at Ising spin glass transitions. These results confirm conclusions drawn from numerical data for dimension 3.

cond-mat.dis-nn↗
arXiv1996

Ordering temperatures and critical exponents in Ising spin glasses

We propose a numerical criterion which can be used to obtain accurate and reliable values of the ordering temperatures and critical exponents of spin glasses. Using this method we find an value of the ordering temperature for the $\pm J$ Ising spin glass in three dimensions which is definitely non-zero and in good agreement with previous estimates. We show that the critical exponents of three dimensional Ising spin glasses do not appear to obey the usual universality rules.

cond-mat↗