Microphase Separation and modulated phases in a Coulomb frustrated Ising ferromagnet

We study a 3-dimensional Ising model in which the tendency to order due to short-range ferromagnetic interactions is frustrated by competing long-range (Coulombic) interactions. Complete ferromagnetic ordering is impossible for any nonzero value of the frustration parameter, but the system displays a variety of phases characterized by periodically modulated structures. We have performed extensive Monte-Carlo simulations which provide strong evidence that the microphase separation transition between paramagnetic and modulated phases is a fluctuation-induced first-order transition. Additional transitions to various commensurate phases may also occur when further lowering the temperature.Comment: 6 pages, 4 figures, accepted in Europhys. Letter

Ensemble Inequivalence and the Spin-Glass Transition

We report on the ensemble inequivalence in a many-body spin-glass model with integer spin. The spin-glass phase transition is of first order for certain values of the crystal field strength and is dependent whether it was derived in the microcanonical or the canonical ensemble. In the limit of infinitely many-body interactions, the model is the integer-spin equivalent of the random-energy model, and is solved exactly. We also derive the integer-spin equivalent of the de Almeida-Thouless line.Comment: 19 pages, 7 figure

Modeling the functional genomics of autism using human neurons.

Human neural progenitors from a variety of sources present new opportunities to model aspects of human neuropsychiatric disease in vitro. Such in vitro models provide the advantages of a human genetic background combined with rapid and easy manipulation, making them highly useful adjuncts to animal models. Here, we examined whether a human neuronal culture system could be utilized to assess the transcriptional program involved in human neural differentiation and to model some of the molecular features of a neurodevelopmental disorder, such as autism. Primary normal human neuronal progenitors (NHNPs) were differentiated into a post-mitotic neuronal state through addition of specific growth factors and whole-genome gene expression was examined throughout a time course of neuronal differentiation. After 4 weeks of differentiation, a significant number of genes associated with autism spectrum disorders (ASDs) are either induced or repressed. This includes the ASD susceptibility gene neurexin 1, which showed a distinct pattern from neurexin 3 in vitro, and which we validated in vivo in fetal human brain. Using weighted gene co-expression network analysis, we visualized the network structure of transcriptional regulation, demonstrating via this unbiased analysis that a significant number of ASD candidate genes are coordinately regulated during the differentiation process. As NHNPs are genetically tractable and manipulable, they can be used to study both the effects of mutations in multiple ASD candidate genes on neuronal differentiation and gene expression in combination with the effects of potential therapeutic molecules. These data also provide a step towards better understanding of the signaling pathways disrupted in ASD

Global Bethe lattice consideration of the spin-1 Ising model

The spin-1 Ising model with bilinear and biquadratic exchange interactions and single-ion crystal field is solved on the Bethe lattice using exact recursion equations. The general procedure of critical properties investigation is discussed and full set of phase diagrams are constructed for both positive and negative biquadratic couplings. In latter case we observe all remarkable features of the model, uncluding doubly-reentrant behavior and ferrimagnetic phase. A comparison with the results of other approximation schemes is done.Comment: Latex, 11 pages, 13 ps figures available upon reques

Ensemble Inequivalence in the Spherical Spin Glass Model with Nonlinear Interactions

We investigate the ensemble inequivalence of the spherical spin glass model with nonlinear interactions of polynomial order $p$. This model is solved exactly for arbitrary $p$ and is shown to have first-order phase transitions between the paramagnetic and spin glass or ferromagnetic phases for $p \geq 5$. In the parameter region around the first-order transitions, the solutions give different results depending on the ensemble used for the analysis. In particular, we observe that the microcanonical specific heat can be negative and the phase may not be uniquely determined by the temperature.Comment: 15 pages, 10 figure

Probing Interband Coulomb Interactions in Semiconductor Nanocrystals with 2D Double-Quantum Coherence Spectroscopy

Using previously developed exciton scattering model accounting for the interband, i.e., exciton-biexciton, Coulomb interactions in semiconductor nanocrystals (NCs), we derive a closed set of equations for 2D double-quantum coherence signal. The signal depends on the Liouville space pathways which include both the interband scattering processes and the inter- and intraband optical transitions. These processes correspond to the formation of different cross-peaks in the 2D spectra. We further report on our numerical calculations of the 2D signal using reduced level scheme parameterized for PbSe NCs. Two different NC excitation regimes considered and unique spectroscopic features associated with the interband Coulomb interactions are identified.Comment: 11 pages, 5 figure

Critical dimensions of the diffusion equation

We study the evolution of a random initial field under pure diffusion in various space dimensions. From numerical calculations we find that the persistence properties of the system show sharp transitions at critical dimensions d1 ~ 26 and d2 ~ 46. We also give refined measurements of the persistence exponents for low dimensions.Comment: 4 pages, 5 figure

Zero frequency divergence and gauge phase factor in the optical response theory

The static current-current correlation leads to the definitional zero frequency divergence (ZFD) in the optical susceptibilities. Previous computations have shown nonequivalent results between two gauges (${\bf p\cdot A}$ and ${\bf E \cdot r}$) under the exact same unperturbed wave functions. We reveal that those problems are caused by the improper treatment of the time-dependent gauge phase factor in the optical response theory. The gauge phase factor, which is conventionally ignored by the theory, is important in solving ZFD and obtaining the equivalent results between these two gauges. The Hamiltonians with these two gauges are not necessary equivalent unless the gauge phase factor is properly considered in the wavefunctions. Both Su-Shrieffer-Heeger (SSH) and Takayama-Lin-Liu-Maki (TLM) models of trans-polyacetylene serve as our illustrative examples to study the linear susceptibility $\chi^{(1)}$ through both current-current and dipole-dipole correlations. Previous improper results of the $\chi^{(1)}$ calculations and distribution functions with both gauges are discussed. The importance of gauge phase factor to solve the ZFD problem is emphasized based on SSH and TLM models. As a conclusion, the reason why dipole-dipole correlation favors over current-current correlation in the practical computations is explained.Comment: 17 pages, 7 figures, submitted to Phys. Rev.

Non-equilibrium stationary state of a two-temperature spin chain

A kinetic one-dimensional Ising model is coupled to two heat baths, such that spins at even (odd) lattice sites experience a temperature $T_{e}$ ($$). Spin flips occur with Glauber-type rates generalised to the case of two temperatures. Driven by the temperature differential, the spin chain settles into a non-equilibrium steady state which corresponds to the stationary solution of a master equation. We construct a perturbation expansion of this master equation in terms of the temperature difference and compute explicitly the first two corrections to the equilibrium Boltzmann distribution. The key result is the emergence of additional spin operators in the steady state, increasing in spatial range and order of spin products. We comment on the violation of detailed balance and entropy production in the steady state.Comment: 11 pages, 1 figure, Revte

Dynamical Renormalization Group Study for a Class of Non-local Interface Equations

We provide a detailed Dynamic Renormalization Group study for a class of stochastic equations that describe non-conserved interface growth mediated by non-local interactions. We consider explicitly both the morphologically stable case, and the less studied case in which pattern formation occurs, for which flat surfaces are linearly unstable to periodic perturbations. We show that the latter leads to non-trivial scaling behavior in an appropriate parameter range when combined with the Kardar-Parisi-Zhang (KPZ) non-linearity, that nevertheless does not correspond to the KPZ universality class. This novel asymptotic behavior is characterized by two scaling laws that fix the critical exponents to dimension-independent values, that agree with previous reports from numerical simulations and experimental systems. We show that the precise form of the linear stabilizing terms does not modify the hydrodynamic behavior of these equations. One of the scaling laws, usually associated with Galilean invariance, is shown to derive from a vertex cancellation that occurs (at least to one loop order) for any choice of linear terms in the equation of motion and is independent on the morphological stability of the surface, hence generalizing this well-known property of the KPZ equation. Moreover, the argument carries over to other systems like the Lai-Das Sarma-Villain equation, in which vertex cancellation is known {\em not to} imply an associated symmetry of the equation.Comment: 34 pages, 9 figures. Journal of Statistical Mechanics: Theory and Experiments (in press