Non-universal dynamics of dimer growing interfaces

A finite temperature version of body-centered solid-on-solid growth models involving attachment and detachment of dimers is discussed in 1+1 dimensions. The dynamic exponent of the growing interface is studied numerically via the spectrum gap of the underlying evolution operator. The finite size scaling of the latter is found to be affected by a standard surface tension term on which the growth rates depend. This non-universal aspect is also corroborated by the growth behavior observed in large scale simulations. By contrast, the roughening exponent remains robust over wide temperature ranges.Comment: 11 pages, 7 figures. v2 with some slight correction

Survival probabilities in time-dependent random walks

We analyze the dynamics of random walks in which the jumping probabilities are periodic {\it time-dependent} functions. In particular, we determine the survival probability of biased walkers who are drifted towards an absorbing boundary. The typical life-time of the walkers is found to decrease with an increment of the oscillation amplitude of the jumping probabilities. We discuss the applicability of the results in the context of complex adaptive systems.Comment: 4 pages, 3 figure

Survival Probabilities of History-Dependent Random Walks

We analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations) in the presence of an absorbing boundary. An analytically solvable model is presented, in which a dynamical phase-transition occurs when the correlation strength parameter \mu reaches a critical value \mu_c. For strong positive correlations, \mu > \mu_c, the survival probability is asymptotically finite, whereas for \mu < \mu_c it decays as a power-law in time (chain length).Comment: 3 pages, 2 figure

Composition-tuned smeared phase transitions

Phase transitions in random systems are smeared if individual spatial regions can order independently of the bulk system. In this paper, we study such smeared phase transitions (both classical and quantum) in substitutional alloys A$_{1-x}$B$_x$ that can be tuned from an ordered phase at composition $x=0$ to a disordered phase at $x=1$. We show that the ordered phase develops a pronounced tail that extends over all compositions $x<1$. Using optimal fluctuation theory, we derive the composition dependence of the order parameter and other quantities in the tail of the smeared phase transition. We also compare our results to computer simulations of a toy model, and we discuss experiments.Comment: 6 pages, 4 eps figures included, final version as publishe

The Logarithmic Triviality of Compact QED Coupled to a Four Fermi Interaction

This is the completion of an exploratory study of Compact lattice Quantum Electrodynamics with a weak four-fermi interaction and four species of massless fermions. In this formulation of Quantum Electrodynamics massless fermions can be simulated directly and Finite Size Scaling analyses can be performed at the theory's chiral symmetry breaking critical point. High statistics simulations on lattices ranging from $8^4$ to $24^4$ yield the equation of state, critical indices, scaling functions and cumulants. The measurements are well fit with the orthodox hypothesis that the theory is logarithmically trivial and its continuum limit suffers from Landau's zero charge problem.Comment: 27 pages, 15 figues and 10 table

Scaling of geometric phases close to quantum phase transition in the XY chain

We show that geometric phase of the ground state in the XY model obeys scaling behavior in the vicinity of a quantum phase transition. In particular we find that geometric phase is non-analytical and its derivative with respect to the field strength diverges at the critical magnetic field. Furthermore, universality in the critical properties of the geometric phase in a family of models is verified. In addition, since quantum phase transition occurs at a level crossing or avoided level crossing and these level structures can be captured by Berry curvature, the established relation between geometric phase and quantum phase transitions is not a specific property of the XY model, but a very general result of many-body systems.Comment: 4 page

Complete high-precision entropic sampling

Monte Carlo simulations using entropic sampling to estimate the number of configurations of a given energy are a valuable alternative to traditional methods. We introduce {\it tomographic} entropic sampling, a scheme which uses multiple studies, starting from different regions of configuration space, to yield precise estimates of the number of configurations over the {\it full range} of energies, {\it without} dividing the latter into subsets or windows. Applied to the Ising model on the square lattice, the method yields the critical temperature to an accuracy of about 0.01%, and critical exponents to 1% or better. Predictions for systems sizes L=10 - 160, for the temperature of the specific heat maximum, and of the specific heat at the critical temperature, are in very close agreement with exact results. For the Ising model on the simple cubic lattice the critical temperature is given to within 0.003% of the best available estimate; the exponent ratios $\beta/\nu$ and $\gamma/\nu$ are given to within about 0.4% and 1%, respectively, of the literature values. In both two and three dimensions, results for the {\it antiferromagnetic} critical point are fully consistent with those of the ferromagnetic transition. Application to the lattice gas with nearest-neighbor exclusion on the square lattice again yields the critical chemical potential and exponent ratios $\beta/\nu$ and $\gamma/\nu$ to good precision.Comment: For a version with figures go to http://www.fisica.ufmg.br/~dickman/transfers/preprints/entsamp2.pd

Phase-Transition in Binary Sequences with Long-Range Correlations

Motivated by novel results in the theory of correlated sequences, we analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations). In our model, the probability for a unit bit in a binary string depends on the fraction of unities preceding it. We show that the system undergoes a dynamical phase-transition from normal diffusion, in which the variance D_L scales as the string's length L, into a super-diffusion phase (D_L ~ L^{1+|alpha|}), when the correlation strength exceeds a critical value. We demonstrate the generality of our results with respect to alternative models, and discuss their applicability to various data, such as coarse-grained DNA sequences, written texts, and financial data.Comment: 4 pages, 4 figure

On the finite-size behavior of systems with asymptotically large critical shift

Exact results of the finite-size behavior of the susceptibility in three-dimensional mean spherical model films under Dirichlet-Dirichlet, Dirichlet-Neumann and Neumann-Neumann boundary conditions are presented. The corresponding scaling functions are explicitly derived and their asymptotics close to, above and below the bulk critical temperature $T_c$ are obtained. The results can be incorporated in the framework of the finite-size scaling theory where the exponent $\lambda$ characterizing the shift of the finite-size critical temperature with respect to $T_c$ is smaller than $1/\nu$, with $\nu$ being the critical exponent of the bulk correlation length.Comment: 24 pages, late