Fluctuation-dissipation relation and the Edwards entropy for a glassy granular compaction model

We analytically study a one dimensional compaction model in the glassy regime. Both correlation and response functions are calculated exactly in the evolving dense and low tapping strength limit, where the density relaxes in a $1/\ln t$ fashion. The response and correlation functions turn out to be connected through a non-equilibrium generalisation of the fluctuation-dissipation theorem. The initial response in the average density to an increase in the tapping strength is shown to be negative, while on longer timescales it is shown to be positive. On short time scales the fluctuation-dissipation theorem governs the relation between correlation and response, and we show that such a relationship also exists for the slow degrees of freedom, albeit with a different temperature. The model is further studied within the statistical theory proposed by Edwards and co-workers, and the Edwards entropy is calculated in the large system limit. The fluctuations described by this approach turn out to match the fluctuations as calculated through the dynamical consideration. We believe this to be the first time these ideas have been analytically confirmed in a non-mean-field model.Comment: 4 pages, 3 figure

Domain wall theory and non-stationarity in driven flow with exclusion

We study the dynamical evolution toward steady state of the stochastic non-equilibrium model known as totally asymmetric simple exclusion process, in both uniform and non-uniform (staggered) one-dimensional systems with open boundaries. Domain-wall theory and numerical simulations are used and, where pertinent, their results are compared to existing mean-field predictions and exact solutions where available. For uniform chains we find that the inclusion of fluctuations inherent to the domain-wall formulation plays a crucial role in providing good agreement with simulations, which is severely lacking in the corresponding mean-field predictions. For alternating-bond chains the domain-wall predictions for the features of the phase diagram in the parameter space of injection and ejection rates turn out to be realized only in an incipient and quantitatively approximate way. Nevertheless, significant quantitative agreement can be found between several additional domain-wall theory predictions and numerics.Comment: 12 pages, 12 figures (published version

Correlation--function distributions at the Nishimori point of two-dimensional Ising spin glasses

The multicritical behavior at the Nishimori point of two-dimensional Ising spin glasses is investigated by using numerical transfer-matrix methods to calculate probability distributions $P(C)$ and associated moments of spin-spin correlation functions $C$ on strips. The angular dependence of the shape of correlation function distributions $P(C)$ provides a stringent test of how well they obey predictions of conformal invariance; and an even symmetry of $(1-C) P(C)$ reflects the consequences of the Ising spin-glass gauge (Nishimori) symmetry. We show that conformal invariance is obeyed in its strictest form, and the associated scaling of the moments of the distribution is examined, in order to assess the validity of a recent conjecture on the exact localization of the Nishimori point. Power law divergences of $P(C)$ are observed near C=1 and C=0, in partial accord with a simple scaling scheme which preserves the gauge symmetry.Comment: Final version to be published in Phys Rev

Dilution effect in correlated electron system with orbital degeneracy

Theory of dilution effect in orbital ordered system is presented. The $e_g$ orbital model without spin degree of freedom and the spin-orbital coupled model in a three-dimensional simple-cubic lattice are analyzed by the Monte-Carlo simulation and the cluster expansion method. In the $e_g$ orbital model without spin degree of freedom, reduction of the orbital ordering temperature due to dilution is steeper than that in the dilute magnet. This is attributed to a modification of the orbital wave-function around vacant sites. In the spin-orbital coupled model, it is found that magnetic structure is changed from the A-type antiferromagnetic order into the ferromagnetic one. Orbital dependent exchange interaction and a sign change of this interaction around vacant sites bring about this novel phenomena. Present results explain the recent experiments in transition-metal compounds with orbital dilution.Comment: 12 pages, 16 figure

Scaling treatment of the random field Ising model

Analytic phenomenological scaling is carried out for the random field Ising model in general dimensions using a bar geometry. Domain wall configurations and their decorated profiles and associated wandering and other exponents $(\zeta,\gamma,\delta,\mu)$ are obtained by free energy minimization. Scaling between different bar widths provides the renormalization group (RG) transformation. Its consequences are (1) criticality at $h=T=0$ in $d \leq 2$ with correlation length $\xi(h,T)$ diverging like $\xi(h,0) \propto h^{-2/(2-d)}$ for $d<2$ and $\xi(h,0) \propto \exp[1/(c_1\gamma h^{\gamma})]$ for $d=2$, where $c_1$ is a decoration constant; (2) criticality in $d = 2+\epsilon$ dimensions at $T=0$, $h^{\ast}= (\epsilon/2c_1)^{1/\gamma}$, where $\xi \propto [(s-s^{\ast})/s]^{-2\epsilon/\gamma}$, $s \equiv h^{\gamma}$. Finite temperature generalizations are outlined. Numerical transfer matrix calculations and results from a ground state algorithm adapted for strips in $d=2$ confirm the ingredients which provide the RG description.Comment: RevTex v3.0, 5 pages, plus 4 figures uuencode

Randomly Diluted e_g Orbital-Ordered Systems

Dilution effects on the long-range ordered state of the doubly degenerate $e_g$ orbital are investigated. Quenched impurities without the orbital degree of freedom are introduced in the orbital model where the long-range order is realized by the order-from-disorder mechanism. It is shown by the Monte-Carlo simulation and the cluster-expansion method that a decrease in the orbital ordering temperature by dilution is remarkable in comparison with that in the randomly diluted spin models. Tiltings of orbitals around impurity cause this unique dilution effects on the orbital systems. The present theory provides a new view point for the recent experiments in KCu$_{1-x}$Zn$_x$F$_3$.Comment: 4 pages, 4 figure