Strongly Asymmetric Tricriticality of Quenched Random-Field Systems

In view of the recently seen dramatic effect of quenched random bonds on tricritical systems, we have conducted a renormalization-group study on the effect of quenched random fields on the tricritical phase diagram of the spin-1 Ising model in $d=3$. We find that random fields convert first-order phase transitions into second-order, in fact more effectively than random bonds. The coexistence region is extremely flat, attesting to an unusually small tricritical exponent $\beta_u$; moreover, an extreme asymmetry of the phase diagram is very striking. To accomodate this asymmetry, the second-order boundary exhibits reentrance.Comment: revtex, 4 pages, 2 figs, submitted to PR

Deep Spin-Glass Hysteresis Area Collapse and Scaling in the d=3d=3 ±J\pm J Ising Model

We investigate the dissipative loss in the $\pm J$ Ising spin glass in three dimensions through the scaling of the hysteresis area, for a maximum magnetic field that is equal to the saturation field. We perform a systematic analysis for the whole range of the bond randomness as a function of the sweep rate, by means of frustration-preserving hard-spin mean field theory. Data collapse within the entirety of the spin-glass phase driven adiabatically (i.e., infinitely-slow field variation) is found, revealing a power-law scaling of the hysteresis area as a function of the antiferromagnetic bond fraction and the temperature. Two dynamic regimes separated by a threshold frequency $\omega_c$ characterize the dependence on the sweep rate of the oscillating field. For $\omega < \omega_c$, the hysteresis area is equal to its value in the adiabatic limit $\omega = 0$, while for $\omega > \omega_c$ it increases with the frequency through another randomness-dependent power law.Comment: 6 pages, 6 figure

Response repetition biases in human perceptual decisions are explained by activity decay in competitive attractor models

Animals and humans have a tendency to repeat recent choices, a phenomenon known as choice hysteresis. The mechanism for this choice bias remains unclear. Using an established, biophysically informed model of a competitive attractor network for decision making, we found that decaying tail activity from the previous trial caused choice hysteresis, especially during difficult trials, and accurately predicted human perceptual choices. In the model, choice variability could be directionally altered through amplification or dampening of post-trial activity decay through simulated depolarizing or hyperpolarizing network stimulation. An analogous intervention using transcranial direct current stimulation (tDCS) over left dorsolateral prefrontal cortex (dlPFC) yielded a close match between model predictions and experimental results: net soma depolarizing currents increased choice hysteresis, while hyperpolarizing currents suppressed it. Residual activity in competitive attractor networks within dlPFC may thus give rise to biases in perceptual choices, which can be directionally controlled through non-invasive brain stimulation

Epistemic consequentialism, truth fairies and worse fairies

Direct Epistemic Consequentialism faces the Truth Fairy. Indirect Epistemic Consequentialism promises to avoid this issue. But there are worse fairies than the Truth Fairy. There is the Worse Fairy. The case of the Worse Fairy helps demonstrate that epistemic consequentialists who would solve problems like the Truth Fairy by ‘going indirect’ face a dilemma

Multicritical Points and Crossover Mediating the Strong Violation of Universality: Wang-Landau Determinations in the Random-Bond d=2d=2 Blume-Capel model

The effects of bond randomness on the phase diagram and critical behavior of the square lattice ferromagnetic Blume-Capel model are discussed. The system is studied in both the pure and disordered versions by the same efficient two-stage Wang-Landau method for many values of the crystal field, restricted here in the second-order phase transition regime of the pure model. For the random-bond version several disorder strengths are considered. We present phase diagram points of both pure and random versions and for a particular disorder strength we locate the emergence of the enhancement of ferromagnetic order observed in an earlier study in the ex-first-order regime. The critical properties of the pure model are contrasted and compared to those of the random model. Accepting, for the weak random version, the assumption of the double logarithmic scenario for the specific heat we attempt to estimate the range of universality between the pure and random-bond models. The behavior of the strong disorder regime is also discussed and a rather complex and yet not fully understood behavior is observed. It is pointed out that this complexity is related to the ground-state structure of the random-bond version.Comment: 12 pages, 11 figures, submitted for publicatio

Phase Transitions in Chemisorbed Systems

Contains reports on two research projects.Joint Services Electronics Program (Contract DAAG29-80-C-0104

Strong Violation of Critical Phenomena Universality: Wang-Landau Study of the 2d Blume-Capel Model under Bond Randomness

We study the pure and random-bond versions of the square lattice ferromagnetic Blume-Capel model, in both the first-order and second-order phase transition regimes of the pure model. Phase transition temperatures, thermal and magnetic critical exponents are determined for lattice sizes in the range L=20-100 via a sophisticated two-stage numerical strategy of entropic sampling in dominant energy subspaces, using mainly the Wang-Landau algorithm. The second-order phase transition, emerging under random bonds from the second-order regime of the pure model, has the same values of critical exponents as the 2d Ising universality class, with the effect of the bond disorder on the specific heat being well described by double-logarithmic corrections, our findings thus supporting the marginal irrelevance of quenched bond randomness. On the other hand, the second-order transition, emerging under bond randomness from the first-order regime of the pure model, has a distinctive universality class with \nu=1.30(6) and \beta/\nu=0.128(5). This amounts to a strong violation of the universality principle of critical phenomena, since these two second-order transitions, with different sets of critical exponents, are between the same ferromagnetic and paramagnetic phases. Furthermore, the latter of these two transitions supports an extensive but weak universality, since it has the same magnetic critical exponent (but a different thermal critical exponent) as a wide variety of two-dimensional systems. In the conversion by bond randomness of the first-order transition of the pure system to second order, we detect, by introducing and evaluating connectivity spin densities, a microsegregation that also explains the increase we find in the phase transition temperature under bond randomness.Comment: Added discussion and references. 10 pages, 6 figures. Published versio

Movement-related beta oscillations show high intra-individual reliability

Oscillatory activity in the beta frequency range (15-30Hz) recorded from human sensorimotor cortex is of increasing interest as a putative biomarker of motor system function and dysfunction. Despite its increasing use in basic and clinical research, surprisingly little is known about the test-retest reliability of spectral power and peak frequency measures of beta oscillatory signals from sensorimotor cortex. Establishing that these beta measures are stable over time in healthy populations is a necessary precursor to their use in the clinic. Here, we used scalp electroencephalography (EEG) to evaluate intra-individual reliability of beta-band oscillations over six sessions, focusing on changes in beta activity during movement (Movement-Related Beta Desynchronization, MRBD) and after movement termination (Post-Movement Beta Rebound, PMBR). Subjects performed visually-cued unimanual wrist flexion and extension. We assessed Intraclass Correlation Coefficients (ICC) and between-session correlations for spectral power and peak frequency measures of movement-related and resting beta activity. Movement-related and resting beta power from both sensorimotor cortices was highly reliable across sessions. Resting beta power yielded highest reliability (average ICC=0.903), followed by MRBD (average ICC=0.886) and PMBR (average ICC=0.663). Notably, peak frequency measures yielded lower ICC values compared to the assessment of spectral power, particularly for movement-related beta activity (ICC=0.386-0.402). Our data highlight that power measures of movement-related beta oscillations are highly reliable, while corresponding peak frequency measures show greater intra-individual variability across sessions. Importantly, our finding that beta power estimates show high intra-individual reliability over time serves to validate the notion that these measures reflect meaningful individual differences that can be utilised in basic research and clinical studies

Excitation Spectrum Gap and Spin-Wave Stiffness of XXZ Heisenberg Chains: Global Renormalization-Group Calculation

The anisotropic XXZ spin-1/2 Heisenberg chain is studied using renormalization-group theory. The specific heats and nearest-neighbor spin-spin correlations are calculated thoughout the entire temperature and anisotropy ranges in both ferromagnetic and antiferromagnetic regions, obtaining a global description and quantitative results. We obtain, for all anisotropies, the antiferromagnetic spin-liquid spin-wave velocity and the Isinglike ferromagnetic excitation spectrum gap, exhibiting the spin-wave to spinon crossover. A number of characteristics of purely quantum nature are found: The in-plane interaction s_i^x s_j^x + s_i^y s_j^y induces an antiferromagnetic correlation in the out-of-plane s_i^z component, at higher temperatures in the antiferromagnetic XXZ chain, dominantly at low temperatures in the ferromagnetic XXZ chain, and, in-between, at all temperatures in the XY chain. We find that the converse effect also occurs in the antiferromagnetic XXZ chain: an antiferromagnetic s_i^z s_j^z interaction induces a correlation in the s_i^xy component. As another purely quantum effect, (i) in the antiferromagnet, the value of the specific heat peak is insensitive to anisotropy and the temperature of the specific heat peak decreases from the isotropic (Heisenberg) with introduction of either type (Ising or XY) anisotropy; (ii) in complete contrast, in the ferromagnet, the value and temperature of the specific heat peak increase with either type of anisotropy.Comment: New results added to text and figures. 12 pages, 18 figures, 3 tables. Published versio

Fractal and Transfractal Recursive Scale-Free Nets

We explore the concepts of self-similarity, dimensionality, and (multi)scaling in a new family of recursive scale-free nets that yield themselves to exact analysis through renormalization techniques. All nets in this family are self-similar and some are fractals - possessing a finite fractal dimension - while others are small world (their diameter grows logarithmically with their size) and are infinite-dimensional. We show how a useful measure of "transfinite" dimension may be defined and applied to the small world nets. Concerning multiscaling, we show how first-passage time for diffusion and resistance between hub (the most connected nodes) scale differently than for other nodes. Despite the different scalings, the Einstein relation between diffusion and conductivity holds separately for hubs and nodes. The transfinite exponents of small world nets obey Einstein relations analogous to those in fractal nets.Comment: Includes small revisions and references added as result of readers' feedbac