Is the droplet theory for the Ising spin glass inconsistent with replica field theory?

Symmetry arguments are used to derive a set of exact identities between irreducible vertex functions for the replica symmetric field theory of the Ising spin glass in zero magnetic field. Their range of applicability spans from mean field to short ranged systems in physical dimensions. The replica symmetric theory is unstable for d>8, just like in mean field theory. For 6<d<8 and d<6 the resummation of an infinite number of terms is necessary to settle the problem. When d<8, these Ward-like identities must be used to distinguish an Almeida-Thouless line from the replica symmetric droplet phase.Comment: 4 pages. Accepted for publication in J.Phys.A. This is the accepted version with the following minor changes: one extra sentence in the abstract; footnote 2 slightly extended; last paragraph somewhat reformulate

The Stability of the Replica Symmetric State in Finite Dimensional Spin Glasses

According to the droplet picture of spin glasses, the low-temperature phase of spin glasses should be replica symmetric. However, analysis of the stability of this state suggested that it was unstable and this instability lends support to the Parisi replica symmetry breaking picture of spin glasses. The finite-size scaling functions in the critical region of spin glasses below T_c in dimensions greater than 6 can be determined and for them the replica symmetric solution is unstable order by order in perturbation theory. Nevertheless the exact solution can be shown to be replica-symmetric. It is suggested that a similar mechanism might apply in the low-temperature phase of spin glasses in less than six dimensions, but that a replica symmetry broken state might exist in more than six dimensions.Comment: 5 pages. Modified to include a paragraph on the relation of this work to that of Newman and Stei

Dynamics of Ordering of Heisenberg Spins with Torque --- Nonconserved Case. I

We study the dynamics of ordering of a nonconserved Heisenberg magnet. The dynamics consists of two parts --- an irreversible dissipation into a heat bath and a reversible precession induced by a torque due to the local molecular field. For quenches to zero temperature, we provide convincing arguments, both numerically (Langevin simulation) and analytically (approximate closure scheme due to Mazenko), that the torque is irrelevant at late times. We subject the Mazenko closure scheme to systematic numerical tests. Such an analysis, carried out for the first time on a vector order parameter, shows that the closure scheme performs respectably well. For quenches to $T_c$, we show, to ${\cal O}(\epsilon^2)$, that the torque is irrelevant at the Wilson-Fisher fixed point.Comment: 13 pages, REVTEX, and 19 .eps figures, compressed, Submitted to Phys. Rev.

Phase Ordering Kinetics with External Fields and Biased Initial Conditions

The late-time phase-ordering kinetics of the O(n) model for a non-conserved order parameter are considered for the case where the O(n) symmetry is broken by the initial conditions or by an external field. An approximate theoretical approach, based on a `gaussian closure' scheme, is developed, and results are obtained for the time-dependence of the mean order parameter, the pair correlation function, the autocorrelation function, and the density of topological defects [e.g. domain walls ($n=1$), or vortices ($n=2$)]. The results are in qualitative agreement with experiments on nematic films and related numerical simulations on the two-dimensional XY model with biased initial conditions.Comment: 35 pages, latex, no figure

Multiscaling to Standard Scaling Crossover in the Bray-Humayun Model for Phase Ordering Kinetics

The Bray-Humayun model for phase ordering dynamics is solved numerically in one and two space dimensions with conserved and non conserved order parameter. The scaling properties are analysed in detail finding the crossover from multiscaling to standard scaling in the conserved case. Both in the nonconserved case and in the conserved case when standard scaling holds the novel feature of an exponential tail in the scaling function is found.Comment: 21 pages, 10 Postscript figure

Sherrington-Kirkpatrick model near T=TcT=T_c: expanding around the Replica Symmetric Solution

An expansion for the free energy functional of the Sherrington-Kirkpatrick (SK) model, around the Replica Symmetric SK solution $Q^{({\rm RS})}_{ab} = \delta_{ab} + q(1-\delta_{ab})$ is investigated. In particular, when the expansion is truncated to fourth order in. $Q_{ab} - Q^{({\rm RS})}_{ab}$. The Full Replica Symmetry Broken (FRSB) solution is explicitly found but it turns out to exist only in the range of temperature $0.549...\leq T\leq T_c=1$, not including T=0. On the other hand an expansion around the paramagnetic solution $Q^{({\rm PM})}_{ab} = \delta_{ab}$ up to fourth order yields a FRSB solution that exists in a limited temperature range $0.915...\leq T \leq T_c=1$.Comment: 18 pages, 3 figure

Dynamical properties of the hypercell spin glass model

The spreading of damage technique is used to study the sensibility to initial conditions in a heath bath Monte Carlo simulation of the spin glass hypercubic cell model. Since the hypercubic cell in dimension 2D and the hypercubic lattice in dimension D resemble each other closely at finite dimensions and both converge to mean field when dimension goes to infinity, it allows us to study the effect of dimensionality on the dynamical behavior of spin glasses.Comment: 13 pages, RevTex, 8 ps figure

Spin glass transition in a magnetic field: a renormalization group study

We study the transition of short range Ising spin glasses in a magnetic field, within a general replica symmetric field theory, which contains three masses and eight cubic couplings, that is defined in terms of the fields representing the replicon, anomalous and longitudinal modes. We discuss the symmetry of the theory in the limit of replica number n to 0, and consider the regular case where the longitudinal and anomalous masses remain degenerate. The spin glass transitions in zero and non-zero field are analyzed in a common framework. The mean field treatment shows the usual results, that is a transition in zero field, where all the modes become critical, and a transition in non-zero field, at the de Almeida-Thouless (AT) line, with only the replicon mode critical. Renormalization group methods are used to study the critical behavior, to order epsilon = 6-d. In the general theory we find a stable fixed-point associated to the spin glass transition in zero field. This fixed-point becomes unstable in the presence of a small magnetic field, and we calculate crossover exponents, which we relate to zero-field critical exponents. In a finite magnetic field, we find no physical stable fixed-point to describe the AT transition, in agreement with previous results of other authors.Comment: 36 pages with 4 tables. To be published in Phys. Rev.

Trematodes of the Great Barrier Reef, Australia: emerging patterns of diversity and richness in coral reef fishes

The Great Barrier Reef holds the richest array of marine life found anywhere in Australia, including a diverse and fascinating parasite fauna. Members of one group, the trematodes, occur as sexually mature adult worms in almost all Great Barrier Reef bony fish species. Although the first reports of these parasites were made 100 years ago, the fauna has been studied systematically for only the last 25 years. When the fauna was last reviewed in 1994 there were 94 species known from the Great Barrier Reef and it was predicted that there might be 2,270 in total. There are now 326 species reported for the region, suggesting that we are in a much improved position to make an accurate prediction of true trematode richness. Here we review the current state of knowledge of the fauna and the ways in which our understanding of this fascinating group is changing. Our best estimate of the true richness is now a range, 1,100–1,800 species. However there remains considerable scope for even these figures to be incorrect given that fewer than one-third of the fish species of the region have been examined for trematodes. Our goal is a comprehensive characterisation of this fauna, and we outline what work needs to be done to achieve this and discuss whether this goal is practically achievable or philosophically justifiable

Phase Ordering Kinetics of One-Dimensional Non-Conserved Scalar Systems

We consider the phase-ordering kinetics of one-dimensional scalar systems. For attractive long-range ($r^{-(1+\sigma)}$) interactions with $\sigma>0$, ``Energy-Scaling'' arguments predict a growth-law of the average domain size $L \sim t^{1/(1+\sigma)}$ for all $\sigma >0$. Numerical results for $\sigma=0.5$, $1.0$, and $1.5$ demonstrate both scaling and the predicted growth laws. For purely short-range interactions, an approach of Nagai and Kawasaki is asymptotically exact. For this case, the equal-time correlations scale, but the time-derivative correlations break scaling. The short-range solution also applies to systems with long-range interactions when $\sigma \rightarrow \infty$, and in that limit the amplitude of the growth law is exactly calculated.Comment: 19 pages, RevTex 3.0, 8 FIGURES UPON REQUEST, 1549