Heisenberg Spin Glass on a Hypercubic Cell

We present results of a Monte Carlo simulation of an Heisenberg Spin Glass model on a hipercubic cell of size 2 in {\it D} dimensions. Each spin interacts with {\it D} nearest neighbors and the lattice is expected to recover the completely connected (mean field) limit as $D\rightarrow \infty$. An analysis of the Binder parameter for $D=8, 9$ and $10$ shows clear evidence of the presence of a spin glass phase at low temperatures. We found that in the high temperature regime the inverse spin glass susceptibility grows linearly with $T^2$ as in the mean field case. Estimates of $T_c$ from the high temperature data are in very good agreement with the results of a Bethe-Peierls approximation for an Heisenberg Spin Glass with coordination number {\it D}.Comment: 6 pages and 4 figures, also available at http://chimera.roma1.infn.it/index_papers_complex.htm

Coarse grained models of stripe forming systems: phase diagrams, anomalies and scaling hypothesis

Two coarse-grained models which capture some universal characteristics of stripe forming systems are stud- ied. At high temperatures, the structure factors of both models attain their maxima on a circle in reciprocal space, as a consequence of generic isotropic competing interactions. Although this is known to lead to some universal properties, we show that the phase diagrams have important differences, which are a consequence of the particular k dependence of the fluctuation spectrum in each model. The phase diagrams are computed in a mean field approximation and also after inclusion of small fluctuations, which are shown to modify drastically the mean field behavior. Observables like the modulation length and magnetization profiles are computed for the whole temperature range accessible to both models and some important differences in behavior are observed. A stripe compression modulus is computed, showing an anomalous behavior with temperature as recently reported in related models. Also, a recently proposed scaling hypothesis for modulated systems is tested and found to be valid for both models studied.Comment: 9 pages, 13 figure

Off equilibrium dynamics of the Frustrated Ising Lattice Gas

We study by means of Monte Carlo simulations the off equilibrium properties of a model glass, the Frustrated Ising Lattice Gas (FILG) in three dimensions. We have computed typical two times quantities, like density-density autocorrelations and the autocorrelation of internal degrees of freedom. We find an aging scenario particularly interesting in the case of the density autocorrelations in real space which is very reminiscent of spin glass phenomenology. While this model captures the essential features of structural glass dynamics, its analogy with spin glasses may bring the possibility of its complete description using the tools developed in spin glass theory.Comment: Phys. Rev. E (Rapid Communication), 1999 (probably May

Index statistical properties of sparse random graphs

Using the replica method, we develop an analytical approach to compute the characteristic function for the probability $\mathcal{P}_N(K,\lambda)$ that a large $N \times N$ adjacency matrix of sparse random graphs has $K$ eigenvalues below a threshold $\lambda$. The method allows to determine, in principle, all moments of $\mathcal{P}_N(K,\lambda)$, from which the typical sample to sample fluctuations can be fully characterized. For random graph models with localized eigenvectors, we show that the index variance scales linearly with $N \gg 1$ for $|\lambda| > 0$, with a model-dependent prefactor that can be exactly calculated. Explicit results are discussed for Erd\"os-R\'enyi and regular random graphs, both exhibiting a prefactor with a non-monotonic behavior as a function of $\lambda$. These results contrast with rotationally invariant random matrices, where the index variance scales only as $\ln N$, with an universal prefactor that is independent of $\lambda$. Numerical diagonalization results confirm the exactness of our approach and, in addition, strongly support the Gaussian nature of the index fluctuations.Comment: 10 pages, 5 figure

Relaxation dynamics of the Ising pp-spin disordered model with finite number of variables

We study the dynamic and metastable properties of the fully connected Ising $p$-spin model with finite number of variables. We define trapping energies, trapping times and self correlation functions and we analyse their statistical properties in comparison to the predictions of trap models.Comment: 7 pages, 6 figures, final versio

Nature of Long-Range Order in Stripe-Forming Systems with Long-Range Repulsive Interactions

We study two dimensional stripe forming systems with competing repulsive interactions decaying as $r^{-\alpha}$. We derive an effective Hamiltonian with a short range part and a generalized dipolar interaction which depends on the exponent $\alpha$. An approximate map of this model to a known XY model with dipolar interactions allows us to conclude that, for $\alpha <2$ long range orientational order of stripes can exist in two dimensions, and establish the universality class of the models. When $\alpha \geq 2$ no long-range order is possible, but a phase transition in the KT universality class is still present. These two different critical scenarios should be observed in experimentally relevant two dimensional systems like electronic liquids ($\alpha=1$) and dipolar magnetic films ($\alpha=3$). Results from Langevin simulations of Coulomb and dipolar systems give support to the theoretical results.Comment: 5 pages, 2 figures. Supplemental Material include