Correct extrapolation of overlap distribution in spin glasses

We study in d=3 dimensions the short range Ising spin glass with Jij=+/-1 couplings at T=0. We show that the overlap distribution is non-trivial in the limit of large system size.Comment: 6 pages, 3 figure

Lack of Ultrametricity in the Low-Temperature phase of 3D Ising Spin Glasses

We study the low-temperature spin-glass phases of the Sherrington-Kirkpatrick (SK) model and of the 3-dimensional short range Ising spin glass (3dISG). For the SK model, evidence for ultrametricity becomes clearer as the system size increases, while for the short-range case our results indicate the opposite, i.e. lack of ultrametricity. Our results are obtained by a recently proposed method that uses clustering to focus on the relevant parts of phase space and reduce finite size effects. Evidence that the mean field solution does not apply in detail to the 3dISG is also found by another method which does not rely on clustering

Discrete energy landscapes and replica symmetry breaking at zero temperature

The order parameter P(q) for disordered systems with degenerate ground-states is reconsidered. We propose that entropy fluctuations lead to a trivial P(q) at zero temperature as in the non-degenerate case, even if there are zero-energy large-scale excitations (complex energy landscape). Such a situation should arise in the 3-dimensional +-J Ising spin glass and in MAX-SAT. Also, we argue that if the energy landscape is complex with a finite number of ground-state families, then replica symmetry breaking reappears at positive temperature.Comment: 7 pages; clarifications on valley definition

State Hierarchy Induced by Correlated Spin Domains in short range spin glasses

We generate equilibrium configurations for the three and four dimensional Ising spin glass with Gaussian distributed couplings at temperatures well below the transition temperature T_c. These states are analyzed by a recently proposed method using clustering. The analysis reveals a hierarchical state space structure. At each level of the hierarchy states are labeled by the orientations of a set of correlated macroscopic spin domains. Our picture of the low temperature phase of short range spin glasses is that of a State Hierarchy Induced by Correlated Spin domains (SHICS). The complexity of the low temperature phase is manifest in the fact that the composition of such a spin domain (i.e. its constituent spins), as well as its identifying label, are defined and determined by the ``location'' in the state hierarchy at which it appears. Mapping out the phase space structure by means of the orientations assumed by these domains enhances our ability to investigate the overlap distribution, which we find to be non-trivial. Evidence is also presented that these states may have a non-ultrametric structure.Comment: 30 pages, 17 figure

Discreteness and entropic fluctuations in GREM-like systems

Within generalized random energy models, we study the effects of energy discreteness and of entropy extensivity in the low temperature phase. At zero temperature, discreteness of the energy induces replica symmetry breaking, in contrast to the continuous case where the ground state is unique. However, when the ground state energy has an extensive entropy, the distribution of overlaps P(q) instead tends towards a single delta function in the large volume limit. Considering now the whole frozen phase, we find that P(q) varies continuously with temperature, and that state-to-state fluctuations of entropy wash out the differences between the discrete and continuous energy models.Comment: 7 pages, 3 figure, 2 figures are added, the volume changes from 4 pages to 7 page

Extension and approximation of mm-subharmonic functions

Let $\Omega\subset \mathbb C^n$ be a bounded domain, and let $f$ be a real-valued function defined on the whole topological boundary $\partial \Omega$. The aim of this paper is to find a characterization of the functions $f$ which can be extended to the inside to a $m$-subharmonic function under suitable assumptions on $\Omega$. We shall do so by using a function algebraic approach with focus on $m$-subharmonic functions defined on compact sets. We end this note with some remarks on approximation of $m$-subharmonic functions

Attractive instability of oppositely charged membranes induced by charge density fluctuations

We predict the conditions under which two oppositely charged membranes show a dynamic, attractive instability. Two layers with unequal charges of opposite sign can repel or be stable when in close proximity. However, dynamic charge density fluctuations can induce an attractive instability and thus facilitate fusion. We predict the dominant instability modes and timescales and show how these are controlled by the relative charge and membrane viscosities. These dynamic instabilities may be the precursors of membrane fusion in systems where artificial vesicles are engulfed by biological cells of opposite charge

Evidence for the double degeneracy of the ground-state in the 3D ±J\pm J spin glass

A bivariate version of the multicanonical Monte Carlo method and its application to the simulation of the three-dimensional $\pm J$ Ising spin glass are described. We found the autocorrelation time associated with this particular multicanonical method was approximately proportional to the system volume, which is a great improvement over previous methods applied to spin-glass simulations. The principal advantage of this version of the multicanonical method, however, was its ability to access information predictive of low-temperature behavior. At low temperatures we found results on the three-dimensional $\pm J$ Ising spin glass consistent with a double degeneracy of the ground-state: the order-parameter distribution function $P(q)$ converged to two delta-function peaks and the Binder parameter approached unity as the system size was increased. With the same density of states used to compute these properties at low temperature, we found their behavior changing as the temperature is increased towards the spin glass transition temperature. Just below this temperature, the behavior is consistent with the standard mean-field picture that has an infinitely degenerate ground state. Using the concept of zero-energy droplets, we also discuss the structure of the ground-state degeneracy. The size distribution of the zero-energy droplets was found to produce the two delta-function peaks of $P(q)$.Comment: 33 pages with 31 eps figures include

Equilibrium valleys in spin glasses at low temperature

We investigate the 3-dimensional Edwards-Anderson spin glass model at low temperature on simple cubic lattices of sizes up to L=12. Our findings show a strong continuity among T>0 physical features and those found previously at T=0, leading to a scenario with emerging mean field like characteristics that are enhanced in the large volume limit. For instance, the picture of space filling sponges seems to survive in the large volume limit at T>0, while entropic effects play a crucial role in determining the free-energy degeneracy of our finite volume states. All of our analysis is applied to equilibrium configurations obtained by a parallel tempering on 512 different disorder realizations. First, we consider the spatial properties of the sites where pairs of independent spin configurations differ and we introduce a modified spin overlap distribution which exhibits a non-trivial limit for large L. Second, after removing the Z_2 (+-1) symmetry, we cluster spin configurations into valleys. On average these valleys have free-energy differences of O(1), but a difference in the (extensive) internal energy that grows significantly with L; there is thus a large interplay between energy and entropy fluctuations. We also find that valleys typically differ by sponge-like space filling clusters, just as found previously for low-energy system-size excitations above the ground state.Comment: 10 pages, 8 figures, RevTeX format. Clarifications and additional reference

Spin Domains Generate Hierarchical Ground State Structure in J=+/-1 Spin Glasses

Unbiased samples of ground states were generated for the short-range Ising spin glass with Jij=+/-1, in three dimensions. Clustering the ground states revealed their hierarchical structure, which is explained by correlated spin domains, serving as cores for macroscopic zero energy "excitations".Comment: 4 pages, 5 figures, accepted to Phys. Rev. Let