Gauge glass in two dimensions

The gauge glass model offers an interesting example of a randomly frustrated system with a continuous O(2) symmetry. In two dimensions, the existence of a glass phase at low temperatures has long been disputed among numerical studies. To resolve this controversy, we examine the behavior of vortices whose movement generates phase slips that destroy phase rigidity at large distances. Detailed analytical and numerical studies of the corresponding Coulomb gas problem in a random potential establish that the ground state, with a finite density of vortices, is polarizable with a scale-dependent dielectric susceptibility. Screening by vortex/antivortex pairs of arbitrarily large size is present to eliminate the logarithmic divergence of the Coulomb energy of a single vortex. The observed power-law decay of the Coulomb interaction between vortices with distance in the ground state leads to a power-law divergence of the glass correlation length with temperature $T$. It is argued that free vortices possess a bound excitation energy and a nonzero diffusion constant at any $T>0$.Comment: 10 pages, no figure, to appear in Proceedings of YKIS 2009 Workshop: Frontiers of Nonequilibrium Physic

Rare-event induced binding transition of heteropolymers

Sequence heterogeneity broadens the binding transition of a polymer onto a linear or planar substrate. This effect is analyzed in a real-space renormalization group scheme designed to capture the statistics of rare events. In the strongly disordered regime, binding initiates at an exponentially rare set of ``good contacts''. Renormalization of the contact potential yields a Kosterlitz-Thouless type transition in any dimension. This and other predictions are confirmed by extensive numerical simulations of a directed polymer interacting with a columnar defect.Comment: 4 pages, 3 figure

Phase transitions of the q-state Potts model on multiply-laced Sierpinski gaskets

We present an exact solution of the q-state Potts model on a class of generalized Sierpinski fractal lattices. The model is shown to possess an ordered phase at low temperatures and a continuous transition to the high temperature disordered phase at any q>=1. Multicriticality is observed in the presence of a symmetry-breaking field. Exact renormalization group analysis yields the phase diagram of the model and a complete set of critical exponents at various transitions.Comment: 6 pages, 6 figures; figures correcte

Finite-size scaling, dynamic fluctuations, and hyperscaling relation in the Kuramoto model

We revisit the Kuramoto model to explore the finite-size scaling (FSS) of the order parameter and its dynamic fluctuations near the onset of the synchronization transition, paying particular attention to effects induced by the randomness of the intrinsic frequencies of oscillators. For a population of size $N$, we study two ways of sampling the intrinsic frequencies according to the {\it same} given unimodal distribution $g(\omega)$. In the `{\em random}' case, frequencies are generated independently in accordance with $g(\omega)$, which gives rise to oscillator number fluctuation within any given frequency interval. In the `{\em regular}' case, the $N$ frequencies are generated in a deterministic manner that minimizes the oscillator number fluctuations, leading to quasi-uniformly spaced frequencies in the population. We find that the two samplings yield substantially different finite-size properties with clearly distinct scaling exponents. Moreover, the hyperscaling relation between the order parameter and its fluctuations is valid in the regular case, but is violated in the random case. In this last case, a self-consistent mean-field theory that completely ignores dynamic fluctuations correctly predicts the FSS exponent of the order parameter but not its critical amplitude

Coordination motifs and large-scale structural organization in atomic clusters

The structure of nanoclusters is complex to describe due to their noncrystallinity, even though bonding and packing constraints limit the local atomic arrangements to only a few types. A computational scheme is presented to extract coordination motifs from sample atomic configurations. The method is based on a clustering analysis of multipole moments for atoms in the first coodination shell. Its power to capture large-scale structural properties is demonstrated by scanning through the ground state of the Lennard-Jones and C$_{60}$ clusters collected at the Cambridge Cluster Database.Comment: 6 pages, 7 figure

Balancing reaction-diffusion network for cell polarization pattern with stability and asymmetry

Cell polarization is a critical process that separates molecules into two distinct regions in prokaryotic and eukaryotic cells, guiding biological processes such as cell division and cell differentiation. Although several underlying antagonistic reaction-diffusion networks capable of setting up cell polarization have been identified experimentally and theoretically, our understanding of how to manipulate pattern stability and asymmetry remains incomplete, especially when only a subset of network components are known. Here we present numerical results to show that the polarized pattern of an antagonistic 2-node network collapses into a homogeneous state when subjected to single-sided self-regulation, single-sided additional regulation, or unequal system parameters. However, polarity can be restored through a combination of two modifications that have opposing effects. Additionally, spatially inhomogeneous parameters favoring respective domains stabilize their interface at designated locations. To connect our findings to cell polarity studies of the nematode Caenorhabditis elegans zygote, we reconstituted a 5-node network where a 4-node circuit with full mutual inhibitions between anterior and posterior is modified by a mutual activation in the anterior and an additional mutual inhibition between the anterior and the posterior. Once again, a generic set of kinetic parameters moves the interface towards either the anterior or posterior end, yet a polarized pattern can be stabilized through spatial tuning of one or more parameters coupled to intracellular or extracellular cues. A user-friendly software, PolarSim, is introduced to facilitate the exploration of networks with alternative node numbers, parameter values, and regulatory pathways