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I. A. Campbell

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

At least 37 records · Page 2Linked to original sources
arXiv2012

The Fortuin-Kasteleyn and Damage Spreading transitions in Random bond Ising lattices

The Fortuin-Kasteleyn and heat-bath damage spreading temperatures T_{FK}(p) and T_{ds}(p) are studied on random bond Ising models of dimension two to five and as functions of the ferromagnetic interaction probability p; the conjecture that T_{ds}(p) ~ T_{FK}(p) is tested. It follows from a statement by Nishimori that in any such system exact coordinates can be given for the intersection point between the Fortuin-Kasteleyn T_{FK}(p) transition line and the Nishimori line, [p_{NL,FK},T_{NL,FK}]. There are no finite size corrections for this intersection point. In dimension three, at the intersection concentration [p_{NL,FK}] the damage spreading T_{ds}(p) is found to be equal to T_{FK}(p) to within 0.1%. For the other dimensions however T_{ds}(p) is observed to be systematically a few percent lower than T_{FK}(p).

cond-mat.stat-mech↗
arXiv2011

Dynamics in the Sherrington-Kirkpatrick Ising spin glass at and above Tg

A detailed numerical study is made of relaxation at equilibrium in the Sherrington-Kirkpatrick Ising spin glass model, at and above the critical temperature Tg. The data show a long time stretched exponential relaxation q(t) ~ exp[-(t/tau(T))^beta(T)] with an exponent beta(T) tending to ~ 1/3 at Tg. The results are compared to those which were observed by Ogielski in the 3d ISG model, and are discussed in terms of a phase space percolation transition scenario.

cond-mat.dis-nn↗
arXiv2011

Stretched exponential behavior and random walks on diluted hypercubic lattices

Diffusion on a diluted hypercube has been proposed as a model for glassy relaxation and is an example of the more general class of stochastic processes on graphs. In this article we determine numerically through large scale simulations the eigenvalue spectra for this stochastic process and calculate explicitly the time evolution for the autocorrelation function and for the return probability, all at criticality, with hypercube dimensions $N$ up to N=28. We show that at long times both relaxation functions can be described by stretched exponentials with exponent 1/3 and a characteristic relaxation time which grows exponentially with dimension $N$. The numerical eigenvalue spectra are consistent with analytic predictions for a generic sparse network model.

cond-mat.stat-mech↗
arXiv2011

Critical scaling to infinite temperature

Three dimensional Ising model ferromagnets on different lattices with nearest neighbor interactions, and on simple cubic lattices with equivalent interactions out to further neighbors, are studied numerically. The susceptibility data for all these systems are analyzed using the critical Renormalization Group Theory formalism over the entire temperature range above Tc with an appropriate choice of scaling variable and scaling expressions. Representative experimental data on a metallic ferromagnet (Ni) and an elementary fluid (Xe) are interpreted in the same manner so as to estimate effective coordination numbers.

cond-mat.stat-mech↗
arXiv2011

An extended scaling analysis of the S=1/2 Ising ferromagnet on the simple cubic lattice

It is often assumed that for treating numerical (or experimental) data on continuous transitions the formal analysis derived from the Renormalization Group Theory can only be applied over a narrow temperature range, the "critical region"; outside this region correction terms proliferate rendering attempts to apply the formalism hopeless. This pessimistic conclusion follows largely from a choice of scaling variables and scaling expressions which is traditional but which is very inefficient for data covering wide temperature ranges. An alternative "extended caling" approach can be made where the choice of scaling variables and scaling expressions is rationalized in the light of well established high temperature series expansion developments. We present the extended scaling approach in detail, and outline the numerical technique used to study the 3d Ising model. After a discussion of the exact expressions for the historic 1d Ising spin chain model as an illustration, an exhaustive analysis of high quality numerical data on the canonical simple cubic lattice 3d Ising model is given. It is shown that in both models, with appropriate scaling variables and scaling expressions (in which leading correction terms are taken into account where necessary), critical behavior extends from Tc up to infinite temperature.

cond-mat.stat-mech↗
arXiv2010

$W$ : an alternative phenomenological coupling parameter for model systems

We introduce a parameter $W(β,L)= (π\,\langle |m| \rangle^2/\langle m^2 \rangle - 2)/(π-2)$ which like the kurtosis (Binder cumulant) is a phenomenological coupling characteristic of the shape of the distribution $p(m)$ of the order parameter $m$. To demonstrate the use of the parameter we analyze extensive numerical data obtained from density of states measurements on the canonical simple cubic spin-$1/2$ Ising ferromagnet, for sizes $L=4$ to $L=256$. Using the $W$-parameter accurate estimates are obtained for the critical inverse temperature $β_c = 0.2216541(2)$, and for the thermal exponent $ν= 0.6308(4)$. In this system at least, corrections to finite size scaling are significantly weaker for the $W$-parameter than for the Binder cumulant.

cond-mat.stat-mech↗
arXiv2009

The Bimodal Ising Spin Glass in dimension three : Corrections to scaling

Equilibrium numerical data on the three dimensional bimodal interaction Ising spin glass up to size L=48 show that corrections to scaling, which are known to be strong, behave in a non-monotonic manner with size. Extrapolation to the infinite size thermodynamic limit is difficult; however the large L data indicate that the ordering temperature Tc lies significantly higher than the values which have been estimated from previous numerical work limited to smaller sizes. In view of the present results it is at the least premature to conclude that the three dimensional bimodal and Gaussian Ising spin glasses lie in the same universality class.

cond-mat.stat-mech↗
arXiv2008

Extended scaling for ferromagnetic Ising models with zero-temperature transitions

We study the second-moment correlation length and the reduced susceptibility of two ferromagnetic Ising models with zero-temperature ordering. By introducing a scaling variable motivated by high-temperature series expansions, we are able to scale data for the one-dimensional Ising ferromagnet rigorously over the entire temperature range. Analogous scaling expressions are then applied to the two-dimensional fully frustrated Villain model where excellent finite-size scaling over the entire temperature range is achieved. Thus we broaden the applicability of the extended scaling method to Ising systems having a zero-temperature critical point.

cond-mat.dis-nn↗
arXiv2008

Extended Scaling for the high dimension and square lattice Ising Ferromagnets

In the high dimension (mean field) limit the susceptibility and the second moment correlation length of the Ising ferromagnet depend on temperature as chi(T)=tau^{-1} and xi(T)=T^{-1/2}tau^{-1/2} exactly over the entire temperature range above the critical temperature T_c, with the scaling variable tau=(T-T_c)/T. For finite dimension ferromagnets temperature dependent effective exponents can be defined over all T using the same expressions. For the canonical two dimensional square lattice Ising ferromagnet it is shown that compact "extended scaling" expressions analogous to the high dimensional limit forms give accurate approximations to the true temperature dependencies, again over the entire temperature range from T_c to infinity. Within this approach there is no cross-over temperature in finite dimensions above which mean-field-like behavior sets in.

cond-mat.stat-mech↗
arXiv2007

Evidence for Two Current Conduction in Iron

Measurements of resistivities of dilute iron based alloys show strong deviations from Matthiessen's rule. These deviations can be explained by a model in which spin up and spin down electrons conduct in parallel. The results are consistent with the theory of impurity shielding in these alloys. [This 1967 paper provides the first experimental demonstration of two current conduction at low temperatures in a ferromagnetic metal. One direct consequence of this property is the Giant Magnetoresistance discovered in 1988 by the groups of Albert Fert and of Peter Grünberg].

cond-mat.mtrl-sci↗
arXiv2007

Extended Scaling for Ferromagnets

A simple systematic rule, inspired by high-temperature series expansion (HTSE) results, is proposed for optimizing the expression for thermodynamic observables of ferromagnets exhibiting critical behavior at $\Tc$. This ``extended scaling'' scheme leads to a protocol for the choice of scaling variables, $τ=(T-\Tc)/T$ or $(T^2 - \Tc^2)/T^2$ depending on the observable instead of $(T-\Tc)/\Tc$, and more importantly to temperature dependent non-critical prefactors for each observable. The rule corresponds to scaling of the leading of the reduced susceptibility above $\Tc$ as $χ_{\rm c}^{*}(T)\sim τ^{-γ}$ in agreement with standard practice with scaling variable $τ$, and for the leading term of the second-moment correlation length as $ξ_{\rm c}^{*}(T)\sim T^{-1/2}τ^{-ν}$. For the specific heat in bipartite lattices the rule gives $C_{\rm c}^{*}(T) \sim T^{-2}[(T^2 -\Tc^2)/T^2]^{-α}$. The latter two expressions are not standard. The scheme can allow for confluent and non-critical correction terms. A stringent test of the extended scaling is made through analyses of high precision numerical and HTSE data, or {\it real} data, on the three-dimensional canonical Ising, XY, and Heisenberg ferromagnets.

cond-mat.stat-mech↗
arXiv2007

Effective critical behavior of the two-dimensional Ising spin glass with bimodal interactions

Monte Carlo data of the two-dimensional Ising spin glass with bimodal interactions are presented with the aim of understanding the low-temperature physics of the model. An analysis of the specific heat, spin-glass susceptibility, finite-size correlation length, and the Binder ratio is performed to try to verify a recent proposal in which for large system sizes and finite but low temperatures the effective critical exponents are identical to the critical exponents of the two-dimensional Ising spin glass with Gaussian interactions. Our results show that with present system sizes the recently proposed scenario in which the two-dimensional Ising spin glass with bimodally distributed interactions is in the same universality class as the model with Gaussian-distributed disorder at low but finite temperatures cannot be reliably proven.

cond-mat.dis-nn↗
arXiv2006

The chiral Anomalous Hall effect in re-entrant AuFe alloys

The Hall effect has been studied in a series of AuFe samples in the re-entrant concentration range, as well as in part of the spin glass range. An anomalous Hall contribution linked to the tilting of the local spins can be identified, confirming theoretical predictions of a novel topological Hall term induced when chirality is present. This effect can be understood in terms of Aharonov-Bohm-like intrinsic current loops arising from successive scatterings by canted local spins. The experimental measurements indicate that the chiral signal persists, meaning scattering within the nanoscopic loops remains coherent, up to temperatures of the order of 150 K.

cond-mat.dis-nn↗
arXiv2006

An Extended Scaling Scheme for Critically Divergent Quantities in Ferromagnets and Spin Glasses

From a consideration of high temperature series expansions in ferromagnets and in spin glasses, we propose an extended scaling scaling scheme involving a set of scaling formulae which express to leading order the temperature (T) and the system size (L) dependences of thermodynamic observables over a much wider range of T than the corresponding one in the conventional scaling scheme. The extended scaling, illustrated by data on the canonical 2d ferromagnet and on the 3d binomial Ising spin glass, leads to consistency for the estimates of critical parameters obtained from scaling analyses for different observables.

cond-mat.stat-mech↗
arXiv2005

Nontrivial critical behavior of the free energy in the two-dimensional Ising spin glass with bimodal interactions

A detailed analysis of Monte Carlo data on the two-dimensional Ising spin glass with bimodal interactions shows that the free energy of the model has a nontrivial scaling. In particular, we show by studying the correlation length that much larger system sizes and lower temperatures are required to see the true critical behavior of the model in the thermodynamic limit. Our results agree with data by Lukic et al. in that the degenerate ground state is separated from the first excited state by an energy gap of 2J.

cond-mat.dis-nn↗
arXiv2005

Dynamic critical behaviour in Ising spin glasses

The critical dynamics of Ising spin glasses with Bimodal, Gaussian, and Laplacian interaction distributions are studied numerically in dimensions 3 and 4. The data demonstrate that in both dimensions the critical dynamic exponent $z_{\rm c}$, the non-equilibrium autocorrelation decay exponent $λ_c/z_{\rm c}$, and the critical fluctuation-dissipation ratio $X_{\infty}$ all vary strongly and systematically with the form of the interaction distribution.

cond-mat.dis-nn↗
arXiv2005

Dynamical scaling in Ising and vector spin glasses

We have studied numerically the dynamics of spin glasses with Ising and XY symmetry (gauge glass) in space dimensions 2, 3, and 4. The nonequilibrium spin-glass susceptibility and the nonequilibrium energy per spin of samples of large size L_b are measured as a function of anneal time t_w after a quench to temperatures T. The two observables are compared to the equilibrium spin-glass susceptibility and the equilibrium energy, respectively, measured as functions of temperature T and system size L for a range of system sizes. For any time and temperature a nonequilibrium time-dependent length scale L*(t_w,T) can be defined by comparing equilibrium and nonequilibrium quantities. Our analysis shows that for all systems studied, an "effective dynamical critical exponent" parametrization L*(t_w,T) = A(T) t^(1/z(T)) fits the data well at each temperature within the whole temperature range studied, which extends from well above the critical temperature to near T = 0 for dimension 2, or to well below the critical temperature for the other space dimensions studied. In addition, the data suggest that the dynamical critical exponent z varies smoothly when crossing the transition temperature.

cond-mat.dis-nn↗