Dynamics of a spherical minority game

We present an exact dynamical solution of a spherical version of the batch minority game (MG) with random external information. The control parameters in this model are the ratio of the number of possible values for the public information over the number of agents, and the radius of the spherical constraint on the microscopic degrees of freedom. We find a phase diagram with three phases: two without anomalous response (an oscillating versus a frozen state), and a further frozen phase with divergent integrated response. In contrast to standard MG versions, we can also calculate the volatility exactly. Our study reveals similarities between the spherical and the conventional MG, but also intriguing differences. Numerical simulations confirm our analytical results.Comment: 16 pages, 3 figures; submitted to J. Phys.

Strategy correlations and timing of adaptation in Minority Games

We study the role of strategy correlations and timing of adaptation for the dynamics of Minority Games, both simulationally and analytically. Using the exact generating functional approach a la De Dominicis we compute the phase diagram and the behaviour of batch and on-line games with correlated strategies, complementing exisiting replica studies of their statics. It is shown that the timing of adaptation can be relevant; while conventional games with uncorrelated strategies are nearly insensitive to the choice of on-line versus batch learning, we find qualitative differences when anti-correlations are present in the strategy assignments. The available standard approximations for the volatility in terms of persistent order parameters in the stationary ergodic states become unreliable in batch games under such circumstances. We then comment on the role of oscillations and the relation to the breakdown of ergodicity. Finally, it is discussed how the generating functional formalism can be used to study mixed populations of so-called `producers' and `speculators' in the context of the batch minority games.Comment: 15 pages, 13 figures, EPJ styl

Magnon Localization in Mattis Glass

We study the spectral and transport properties of magnons in a model of a disordered magnet called Mattis glass, at vanishing average magnetization. We find that in two dimensional space, the magnons are localized with the localization length which diverges as a power of frequency at small frequencies. In three dimensional space, the long wavelength magnons are delocalized. In the delocalized regime in 3d (and also in 2d in a box whose size is smaller than the relevant localization length scale) the magnons move diffusively. The diffusion constant diverges at small frequencies. However, the divergence is slow enough so that the thermal conductivity of a Mattis glass is finite, and we evaluate it in this paper. This situation can be contrasted with that of phonons in structural glasses whose contribution to thermal conductivity is known to diverge (when inelastic scattering is neglected).Comment: 11 page

Glassy behaviour in a simple topological model

In this article we study a simple, purely topological, cellular model which is allowed to evolve through a Glauber-Kawasaki process. We find a non-thermodynamic transition to a glassy phase in which the energy (defined as the square of the local cell topological charge) fails to reach the equilibrium value below a characteristic temperature which is dependent on the cooling rate. We investigate a correlation function which exhibits aging behaviour, and follows a master curve in the stationary regime when time is rescaled by a factor of the relaxation time t_r. This master curve can be fitted by a von Schweidler law in the late beta-relaxation regime. The relaxation times can be well-fitted at all temperatures by an offset Arrhenius law. A power law can be fitted to an intermediate temperature regime; the exponent of the power law and the von Schweidler law roughly agree with the relationship predicted by Mode-coupling Theory. By defining a suitable response function, we find that the fluctuation-dissipation ratio is held until sometime later than the appearance of the plateaux; non-monotonicity of the response is observed after this ratio is broken, a feature which has been observed in other models with dynamics involving activated processes.Comment: 11 pages LaTeX; minor textual corrcetions, minor corrections to figs 4 & 7

Following microscopic motion in a two dimensional glass-forming binary fluid

The dynamics of a binary mixture of large and small discs are studied at temperatures approaching the glass transition using an analysis based on the topology of the Voronoi polygon surrounding each atom. At higher temperatures we find that dynamics is dominated by fluid-like motion that involves particles entering and exiting the nearest-neighbour shells of nearby particles. As the temperature is lowered, the rate of topological moves decreases and motion becomes localised to regions of mixed pentagons and heptagons. In addition we find that in the low temperature state particles may translate significant distances without undergoing changes in their nearest neig hbour shell. These results have implications for dynamical heterogeneities in glass forming liquids.Comment: 12 pages, 7 figure

Modified TAP equations for the SK spin glass

The stability of the TAP mean field equations is reanalyzed with the conclusion that the exclusive reason for the breakdown at the spin glass instability is an inconsistency for the value of the local susceptibility. A new alternative approach leads to modified equations which are in complete agreement with the original ones above the instability. Essentially altered results below the instability are presented and the consequences for the dynamical mean field equations are discussed.Comment: 7 pages, 2 figures, final revised version to appear in Europhys. Let

Aging dynamics in reentrant ferromagnet: Cu0.2_{0.2}Co0.8_{0.8}Cl2_{2}-FeCl3_{3} graphite bi-intercalation compound

Aging dynamics of a reentrant ferromagnet Cu$_{0.2}$Co$_{0.8}$Cl$_{2}$-FeCl$_{3}$ graphite bi-intercalation compound has been studied using AC and DC magnetic susceptibility. This compound undergoes successive transitions at the transition temperatures $T_{c}$ ($= 9.7$ K) and $T_{RSG}$ ($= 3.5$ K). The relaxation rate $S(t)$ exhibits a characteristic peak at $t_{cr}$ close to a wait time $t_{w}$ below $T_{c}$, indicating that the aging phenomena occur in both the reentrant spin glass (RSG) phase below $T_{RSG}$ and the ferromagnetic (FM) phase between $T_{RSG}$ and $T_{c}$. The relaxation rate $S(t)$ ($=\text{d}\chi_{ZFC}(t)/\text{d}\ln t$) in the FM phase exhibits two peaks around $t_{w}$ and a time much shorter than $t_{w}$ under the positive $T$-shift aging, indicating a partial rejuvenation of domains. The aging state in the FM phase is fragile against a weak magnetic-field perturbation. The time ($t$) dependence of $\chi_{ZFC}(t)$ around $t \approx t_{cr}$ is well approximated by a stretched exponential relaxation: $\chi_{ZFC}(t) \approx \exp[-(t/\tau)^{1-n}]$. The exponent $n$ depends on $t_{w}$, $T$, and $H$. The relaxation time $\tau$ ($\approx t_{cr}$) exhibits a local maximum around 5 K, reflecting a chaotic nature of the FM phase. It drastically increases with decreasing temperature below $T_{RSG}$.Comment: 16 pages,16 figures, submitted to Physical Review

The Ising spin glass in finite dimensions: a perturbative study of the free energy

Replica field theory is used to study the n-dependent free energy of the Ising spin glass in a first order perturbative treatment. Large sample-to-sample deviations of the free energy from its quenched average prove to be Gaussian, independently of the special structure of the order parameter. The free energy difference between the replica symmetric and (infinite level) replica symmetry broken phases is studied in details: the line n(T) where it is zero coincides with the Almeida-Thouless line for d>8. The dimensional domain 6<d<8 is more complicated, and several scenarios are possible.Comment: 23 page

Application of the quantum spin glass theory to image restoration

Quantum fluctuation is introduced into the Markov random fields (MRF's) model for image restoration in the context of Bayesian approach. We investigate the dependence of the quantum fluctuation on the quality of BW image restoration by making use of statistical mechanics. We find that the maximum posterior marginal (MPM) estimate based on the quantum fluctuation gives a fine restoration in comparison with the maximum a posterior (MAP) estimate or the thermal fluctuation based MPM estimate.Comment: 19 pages, 9 figures, 1 table, RevTe

Exact solution of a 2d random Ising model

The model considered is a d=2 layered random Ising system on a square lattice with nearest neighbours interaction. It is assumed that all the vertical couplings are equal and take the positive value J while the horizontal couplings are quenched random variables which are equal in the same row but can take the two possible values J and J-K in different rows. The exact solution is obtained in the limit case of infinite K for any distribution of the horizontal couplings. The model which corresponds to this limit can be seen as an ordinary Ising system where the spins of some rows, chosen at random, are frozen in an antiferromagnetic order. No phase transition is found if the horizontal couplings are independent random variables while for correlated disorder one finds a low temperature phase with some glassy properties.Comment: 10 pages, Plain TeX, 3 ps figures, submitted to Europhys. Let