Reply to "Comment on Evidence for the droplet picture of spin glasses"

Using Monte Carlo simulations (MCS) and the Migdal-Kadanoff approximation (MKA), Marinari et al. study in their comment on our paper the link overlap between two replicas of a three-dimensional Ising spin glass in the presence of a coupling between the replicas. They claim that the results of the MCS indicate replica symmetry breaking (RSB), while those of the MKA are trivial, and that moderate size lattices display the true low temperature behavior. Here we show that these claims are incorrect, and that the results of MCS and MKA both can be explained within the droplet picture.Comment: 1 page, 1 figur

Phase Ordering Dynamics of the O(n) Model - Exact Predictions and Numerical Results

We consider the pair correlation functions of both the order parameter field and its square for phase ordering in the $O(n)$ model with nonconserved order parameter, in spatial dimension $2\le d\le 3$ and spin dimension $1\le n\le d$. We calculate, in the scaling limit, the exact short-distance singularities of these correlation functions and compare these predictions to numerical simulations. Our results suggest that the scaling hypothesis does not hold for the $d=2$ $O(2)$ model. Figures (23) are available on request - email [email protected]: 23 pages, Plain LaTeX, M/C.TH.93/2

Drowsy Cheetah Hunting Antelopes: A Diffusing Predator Seeking Fleeing Prey

We consider a system of three random walkers (a `cheetah' surrounded by two `antelopes') diffusing in one dimension. The cheetah and the antelopes diffuse, but the antelopes experience in addition a deterministic relative drift velocity, away from the cheetah, proportional to their distance from the cheetah, such that they tend to move away from the cheetah with increasing time. Using the backward Fokker-Planck equation we calculate, as a function of their initial separations, the probability that the cheetah has caught neither antelope after infinite time.Comment: 5 page

Comment on "General Method to Determine Replica Symmetry Breaking Transitions"

In a recent letter Marinari et al [Phys. Rev. Lett. 81, 1698 (1998)] introduced a new method to study spin glass transitions and argued that by probing replica symmetry (RS) as opposed to time reversal symmetry (TRS), their method unambiguously shows that replica symmetry breaking (RSB) occurs in short-range spin glasses. In this comment we show that while the new method is indeed useful for studying transitions in systems where TRS is absent (such as the p-spin model studied by them), the conclusion that it shows the existence of RSB in short-range spin glasses is wrong.Comment: 1 page, RevTe

The de Almeida-Thouless line in vector spin glasses

We consider the infinite-range spin glass in which the spins have m > 1 components (a vector spin glass). Applying a magnetic field which is random in direction, there is an Almeida Thouless (AT) line below which the "replica symmetric" solution is unstable, just as for the Ising (m=1) case. We calculate the location of this AT line for Gaussian random fields for arbitrary m, and verify our results by numerical simulations for m = 3$.Comment: 19 pages, 4 eps figure

Stress-free Spatial Anisotropy in Phase-Ordering

We find spatial anisotropy in the asymptotic correlations of two-dimensional Ising models under non-equilibrium phase-ordering. Anisotropy is seen for critical and off-critical quenches and both conserved and non-conserved dynamics. We argue that spatial anisotropy is generic for scalar systems (including Potts models) with an anisotropic surface tension. Correlation functions will not be universal in these systems since anisotropy will depend on, e.g., temperature, microscopic interactions and dynamics, disorder, and frustration.Comment: 4 pages, 4 figures include

Evidence for the droplet/scaling picture of spin glasses

We have studied the Parisi overlap distribution for the three dimensional Ising spin glass in the Migdal-Kadanoff approximation. For temperatures T around 0.7Tc and system sizes upto L=32, we found a P(q) as expected for the full Parisi replica symmetry breaking, just as was also observed in recent Monte Carlo simulations on a cubic lattice. However, for lower temperatures our data agree with predictions from the droplet or scaling picture. The failure to see droplet model behaviour in Monte Carlo simulations is due to the fact that all existing simulations have been done at temperatures too close to the transition temperature so that sytem sizes larger than the correlation length have not been achieved.Comment: 4 pages, 6 figure

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

Sex distribution of offspring-parents obesity: Angel's hypothesis revisited

This study, which is based on two cross sectional surveys' data, aims to establish any effect of parental obesity sex distribution of offspring and to replicate the results that led to the hypothesis that obesity may be associated with sex-linked recessive lethal gene. A representative sample of 4,064 couples living in Renfrew/Paisley, Scotland was surveyed 1972-1976. A total of 2,338 offspring from 1,477 of the couples screened in 1972-1976, living in Paisley, were surveyed in 1996. In this study, males represented 47.7% among the total offspring of the couples screened in 1972-1976. In the first survey there was a higher male proportion of offspring (53%, p &lt; 0.05) from parents who were both obese, yet this was not significant after adjustment for age of parents. Also, there were no other significant differences in sex distribution of offspring according to body mass index, age, or social class of parents. The conditions of the original 1949 study of Angel (1949) (which proposed a sex-linked lethal recessive gene) were simulated by selecting couples with at least one obese daughter. In this subset, (n = 409), obesity in fathers and mothers was associated with 26% of offspring being male compared with 19% of offspring from a non-obese father and obese mother. Finally we conclude that families with an obese father have a higher proportion of male offspring. These results do not support the long-established hypotheses of a sex-linked recessive lethal gene in the etiology of obesity

Correlated random fields in dielectric and spin glasses

Both orientational glasses and dipolar glasses possess an intrinsic random field, coming from the volume difference between impurity and host ions. We show this suppresses the glass transition, causing instead a crossover to the low $T$ phase. Moreover the random field is correlated with the inter-impurity interactions, and has a broad distribution. This leads to a peculiar variant of the Imry-Ma mechanism, with 'domains' of impurities oriented by a few frozen pairs. These domains are small: predictions of domain size are given for specific systems, and their possible experimental verification is outlined. In magnetic glasses in zero field the glass transition survives, because the random fields are disallowed by time-reversal symmetry; applying a magnetic field then generates random fields, and suppresses the spin glass transition.Comment: minor modifications, final versio