Monte Carlo Study of Cluster-Diameter Distribution: A New Observable to Estimate Correlation Lengths

We report numerical simulations of two-dimensional $q$-state Potts models with emphasis on a new quantity for the computation of spatial correlation lengths. This quantity is the cluster-diameter distribution function $G_{diam}(x)$, which measures the distribution of the diameter of stochastically defined cluster. Theoretically it is predicted to fall off exponentially for large diameter $x$, $G_{diam} \propto \exp(-x/\xi)$, where $\xi$ is the correlation length as usually defined through the large-distance behavior of two-point correlation functions. The results of our extensive Monte Carlo study in the disordered phase of the models with $q=10$, 15, and $20$ on large square lattices of size $300 \times 300$, $120 \times 120$, and $80 \times 80$, respectively, clearly confirm the theoretically predicted behavior. Moreover, using this observable we are able to verify an exact formula for the correlation length $\xi_d(\beta_t)$ in the disordered phase at the first-order transition point $\beta_t$ with an accuracy of about $1$ for all considered values of $q$. This is a considerable improvement over estimates derived from the large-distance behavior of standard (projected) two-point correlation functions, which are also discussed for comparison.Comment: 20 pages, LaTeX + 13 postscript figures. See also http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm

Dynamics of Phase Transitions by Hysteresis Methods I

In studies of the QCD deconfining phase transition or crossover by means of heavy ion experiments, one ought to be concerned about non-equilibrium effects due to heating and cooling of the system. Motivated by this, we look at hysteresis methods to study the dynamics of phase transitions. Our systems are temperature driven through the phase transition using updating procedures in the Glauber universality class. Hysteresis calculations are presented for a number of observables, including the (internal) energy, properties of Fortuin-Kasteleyn clusters and structure functions. We test the methods for 2d Potts models, which provide a rich collection of phase transitions with a number of rigorously known properties. Comparing with equilibrium configurations we find a scenario where the dynamics of the transition leads to a spinodal decomposition which dominates the statistical properties of the configurations. One may expect an enhancement of low energy gluon production due to spinodal decomposition of the Polyakov loops, if such a scenario is realized by nature.Comment: 12 pages, revised after referee report, to appear in Phys. Rev.

Thermal properties of gauge-fields common to anyon superconductors and spin-liquids

The thermally driven confinement-deconfinement transition exhibited by lattice quantum electrodynamics in two space dimensions is re-examined in the context of the statistical gauge-fields common to anyon superconductors and to spin-liquids. Particle-hole excitations in both systems are bound by a confining string at temperatures below the transition temperature $T_c$. We argue that $T_c$ coincides with the actual critical temperature for anyon superconductivity. The corresponding specific-heat contribution, however, shows a {\it smooth} peak just below $T_c$ characteristic of certain high-temperature superconductors.Comment: 13 pgs, TeX, to appear in Physical Review B (minor revisions

Protein sequence and structure: Is one more fundamental than the other?

We argue that protein native state structures reside in a novel "phase" of matter which confers on proteins their many amazing characteristics. This phase arises from the common features of all globular proteins and is characterized by a sequence-independent free energy landscape with relatively few low energy minima with funnel-like character. The choice of a sequence that fits well into one of these predetermined structures facilitates rapid and cooperative folding. Our model calculations show that this novel phase facilitates the formation of an efficient route for sequence design starting from random peptides.Comment: 7 pages, 4 figures, to appear in J. Stat. Phy

A review of Monte Carlo simulations of polymers with PERM

In this review, we describe applications of the pruned-enriched Rosenbluth method (PERM), a sequential Monte Carlo algorithm with resampling, to various problems in polymer physics. PERM produces samples according to any given prescribed weight distribution, by growing configurations step by step with controlled bias, and correcting "bad" configurations by "population control". The latter is implemented, in contrast to other population based algorithms like e.g. genetic algorithms, by depth-first recursion which avoids storing all members of the population at the same time in computer memory. The problems we discuss all concern single polymers (with one exception), but under various conditions: Homopolymers in good solvents and at the $\Theta$ point, semi-stiff polymers, polymers in confining geometries, stretched polymers undergoing a forced globule-linear transition, star polymers, bottle brushes, lattice animals as a model for randomly branched polymers, DNA melting, and finally -- as the only system at low temperatures, lattice heteropolymers as simple models for protein folding. PERM is for some of these problems the method of choice, but it can also fail. We discuss how to recognize when a result is reliable, and we discuss also some types of bias that can be crucial in guiding the growth into the right directions.Comment: 29 pages, 26 figures, to be published in J. Stat. Phys. (2011

Phase transition in spin systems with various types of fluctuations

Various types ordering processes in systems with large fluctuation are overviewed. Generally, the so-called order–disorder phase transition takes place in competition between the interaction causing the system be ordered and the entropy causing a random disturbance. Nature of the phase transition strongly depends on the type of fluctuation which is determined by the structure of the order parameter of the system. As to the critical property of phase transitions, the concept “universality of the critical phenomena” is well established. However, we still find variety of features of ordering processes. In this article, we study effects of various mechanisms which bring large fluctuation in the system, e.g., continuous symmetry of the spin in low dimensions, contradictions among interactions (frustration), randomness of the lattice, quantum fluctuations, and a long range interaction in off-lattice systems

Psychopathology and temperament in parents and offspring: results of a family study.

BACKGROUND: Although research on the association between temperament and psychopathology has received renewed interest, few investigations have addressed the issues of psychiatric comorbidity or the role of temperament across the life span. The present investigation employed a family study/high-risk design to examine the specificity of associations between temperamental traits and psychiatric disorders in both children and adults. METHODS: The sample was composed of 244 probands and 82 children (ages 7-17) from the Yale Family Study of Comorbidity of Substance Abuse and Anxiety. Psychiatric disorders were assessed using structured diagnostic interviews administered by clinicians, and temperament was measured using the Dimensions of Temperament Survey. RESULTS: In both adults and children, anxiety and depression were generally associated with low scores on adaptability and approach/withdrawal, while externalizing or substance use disorders were associated with low attention scores and higher activity. However, psychiatric comorbidity was associated with the manifestation of both clusters of temperamental traits and far greater impairment and clinical severity. Some temperamental characteristics in children also demonstrated specificity of association with parental psychiatric disorder. LIMITATIONS: This investigation was limited to the analysis of cross-sectional data and was unable to separate genetic from other familial risk factors. CONCLUSIONS: The results suggest that temperament remains associated with psychopathology across the life span and may reflect diverse familial influences. Clinical intervention and prevention efforts may benefit from focusing on individuals at higher risk for psychiatric disorder through parental psychopathology or the expression of temperament problems in childhood

Harmonic Pinnacles in the Discrete Gaussian Model

The 2D Discrete Gaussian model gives each height function (Formula presented.) a probability proportional to (Formula presented.), where (Formula presented.) is the inverse-temperature and (Formula presented.) sums over nearest-neighbor bonds. We consider the model at large fixed (Formula presented.), where it is flat unlike its continuous analog (the Discrete Gaussian Free Field). We first establish that the maximum height in an (Formula presented.) box with 0 boundary conditions concentrates on two integers M, M + 1 with (Formula presented.). The key is a large deviation estimate for the height at the origin in (Formula presented.), dominated by “harmonic pinnacles”, integer approximations of a harmonic variational problem. Second, in this model conditioned on (Formula presented.) (a floor), the average height rises, and in fact the height of almost all sites concentrates on levels H, H + 1 where (Formula presented.). This in particular pins down the asymptotics, and corrects the order, in results of Bricmont et al. (J. Stat. Phys. 42(5–6):743–798, 1986), where it was argued that the maximum and the height of the surface above a floor are both of order (Formula presented.). Finally, our methods extend to other classical surface models (e.g., restricted SOS), featuring connections to p-harmonic analysis and alternating sign matrices