On infrared divergences in spin glasses

By studying the structure of infrared divergences in a toy propagator in the replica approach to the Ising spin glass below $T_c$, we suggest a possible cancellation mechanism which could decrease the degree of singularity in the loop expansion.Comment: 13 pages, Latex , revised versio

Symmetry breaking via fermion 4-point functions

We construct the effective action and gap equations for nonperturbative fermion 4-point functions. Our results apply to situations in which fermion masses can be ignored, which is the case for theories of strong flavor interactions involving standard quarks and leptons above the electroweak scale. The structure of the gap equations is different from what a naive generalization of the 2-point case would suggest, and we find for example that gauge exchanges are insufficient to generate nonperturbative 4-point functions when the number of colors is large.Comment: 36 pages, uses Revtex and eps files for figure

Local excitations in mean field spin glasses

We address the question of geometrical as well as energetic properties of local excitations in mean field Ising spin glasses. We study analytically the Random Energy Model and numerically a dilute mean field model, first on tree-like graphs, equivalent to a replica symmetric computation, and then directly on finite connectivity random lattices. In the first model, characterized by a discontinuous replica symmetry breaking, we found that the energy of finite volume excitation is infinite whereas in the dilute mean field model, described by a continuous replica symmetry breaking, it slowly decreases with sizes and saturates at a finite value, in contrast with what would be naively expected. The geometrical properties of these excitations are similar to those of lattice animals or branched polymers. We discuss the meaning of these results in terms of replica symmetry breaking and also possible relevance in finite dimensional systems.Comment: 7 pages, 4 figures, accepted for publicatio

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

Quenched Random Graphs

Spin models on quenched random graphs are related to many important optimization problems. We give a new derivation of their mean-field equations that elucidates the role of the natural order parameter in these models.Comment: 9 pages, report CPTH-A264.109

Comment on ``Critical behavior of a two-species reaction-diffusion problem''

In a recent paper, de Freitas et al. [Phys. Rev. E 61, 6330 (2000)] presented simulational results for the critical exponents of the two-species reaction-diffusion system A + B -> 2B and B -> A in dimension d = 1. In particular, the correlation length exponent was found as \nu = 2.21(5) in contradiction to the exact relation \nu = 2/d. In this Comment, the symmetry arguments leading to exact critical exponents for the universality class of this reaction-diffusion system are concisely reconsidered

Total phallic reconstruction after penile amputation for donkey bite: Case report and review of the literature

There are very few reported cases of traumatic amputation of the male genitalia due to animal bite. The management involves thorough washout of the wounds, debridement, antibiotic prophylaxis, tetanus and rabies immunization followed by immediate reconstruction or primary wound closure with delayed reconstruction, when immediate reconstruction is not feasible. When immediate reconstruction is not feasible, long-term good functional and cosmetic results are still possible in the majority of cases by performing total phallic reconstruction. In particular, it is now possible to fashion a cosmetically acceptable sensate phallus with incorporated neourethra, to allow the patient to void while standing and to ejaculate, and with enough bulk to allow the insertion of a penile prosthesis to guarantee the rigidity necessary to engage in penetrative sexual intercourse

Absence of an equilibrium ferromagnetic spin glass phase in three dimensions

Using ground state computations, we study the transition from a spin glass to a ferromagnet in 3-d spin glasses when changing the mean value of the spin-spin interaction. We find good evidence for replica symmetry breaking up till the critical value where ferromagnetic ordering sets in, and no ferromagnetic spin glass phase. This phase diagram is in conflict with the droplet/scaling and mean field theories of spin glasses. We also find that the exponents of the second order ferromagnetic transition do not depend on the microscopic Hamiltonian, suggesting universality of this transition.Comment: 4 pages, 5 figures, revte

Enhancing the Detection of Natural Thermal Entanglement with Disorder

Physical systems have some degree of disorder present in them. We discuss how to treat natural, thermal entanglement in any random macroscopic system from which a thermodynamic witness bounded by a constant can be found. We propose that functional many-body perturbation theory be applied to allow either a quenched or an annealed average over the disorder to be taken. We find when considering the example of an XX Heisenberg spin chain with a random coupling strength, that the region of natural entanglement detected by both witnesses can be enhanced by the disorder.Comment: 4 pages, 2 figures, accepted by Physical Review Letter

Stability of the Parisi Solution for the Sherrington-Kirkpatrick model near T=0

To test the stability of the Parisi solution near T=0, we study the spectrum of the Hessian of the Sherrington-Kirkpatrick model near T=0, whose eigenvalues are the masses of the bare propagators in the expansion around the mean-field solution. In the limit $T\ll 1$ two regions can be identified. In the first region, for $x$ close to 0, where $x$ is the Parisi replica symmetry breaking scheme parameter, the spectrum of the Hessian is not trivial and maintains the structure of the full replica symmetry breaking state found at higher temperatures. In the second region $T\ll x \leq 1$ as $T\to 0$, the components of the Hessian become insensitive to changes of the overlaps and the bands typical of the full replica symmetry breaking state collapse. In this region only two eigenvalues are found: a null one and a positive one, ensuring stability for $T\ll 1$. In the limit $T\to 0$ the width of the first region shrinks to zero and only the positive and null eigenvalues survive. As byproduct we enlighten the close analogy between the static Parisi replica symmetry breaking scheme and the multiple time-scales approach of dynamics, and compute the static susceptibility showing that it equals the static limit of the dynamic susceptibility computed via the modified fluctuation dissipation theorem.Comment: 24 pages, 6 figures, J. Phys. A (in press