Modeling future cliff-front waves during sea level rise and implications for coastal cliff retreat rates

It is often assumed that future coastal cliff retreat rates will accelerate as global sea level rises, but few studies have investigated how SLR (sea level rise) might change cliff-front wave dynamics. Using a new simple numerical model, this study simulates the number and type (breaking, broken, or unbroken) of cliff-front waves under future SLR scenarios. Previous research shows breaking waves deliver more energy to cliffs than broken waves, and unbroken waves generate minimal impact. Here, we investigated six cliff-platform profiles from three regions (USA, New Zealand, and UK) with varied tidal ranges and wave climates. Model inputs included 2013-2100 hindcast/forecast incident wave height and tidal water level, and three future SLR scenarios. Results show the number of both cliff-front breaking and broken waves generally increase for a high-elevation (relative to tide) cliff-platform junction. In contrast, breaking/broken wave occurrence decrease by 38-92% for a near-horizontal shore platform with a low-elevation cliff-platform junction under a high SRL scenario, leading to high (96-97%) unbroken wave occurrence. Overall, results suggest the response of cliff-front waves to future SLR is complex and depends on shore platform geometries and SLR scenarios, indicating that future cliff retreat rates may not homogeneously accelerate under SLR.

L-cysteine ethylester reverses the adverse effects of morphine on breathing and arterial blood-gas chemistry while minimally affecting antinociception in unanesthetized rats

L-cysteine ethylester (L-CYSee) is a membrane-permeable analogue of L-cysteine with a variety of pharmacological effects. The purpose of this study was to determine the effects of L-CYSee on morphine-induced changes in ventilation, arterial-blood gas (ABG) chemistry, Alveolar-arterial (A-a) gradient (i.e., a measure of the index of alveolar gas-exchange), antinociception and sedation in male Sprague Dawley rats. An injection of morphine (10 mg/kg, IV) produced adverse effects on breathing, including sustained decreases in minute ventilation. L-CYSee (500 μmol/kg, IV) given 15 min later immediately reversed the actions of morphine. Another injection of L-CYSee (500 μmol/kg, IV) after 15 min elicited more pronounced excitatory ventilatory responses. L-CYSee (250 or 500 μmol/kg, IV) elicited a rapid and prolonged reversal of the actions of morphine (10 mg/kg, IV) on ABG chemistry (pH, pCO2, pO2, sO2) and A-a gradient. L-serine ethylester (an oxygen atom replaces the sulfur; 500 μmol/kg, IV), was ineffective in all studies. L-CYSee (500 μmol/kg, IV) did not alter morphine (10 mg/kg, IV)-induced sedation, but slightly reduced the overall duration of morphine (5 or 10 mg/kg, IV)-induced analgesia. In summary, L-CYSee rapidly overcame the effects of morphine on breathing and alveolar gas-exchange, while not affecting morphine sedation or early-stage analgesia. The mechanisms by which L-CYSee modulates morphine depression of breathing are unknown, but appear to require thiol-dependent processes.

Metastate analysis of the ground states of two-dimensional Ising spin glasses

Using an efficient polynomial-time ground-state algorithm we investigate the Ising spin glass state at zero temperature in two dimensions. For large sizes, we show that the spin state in a central region is independent of the interactions far away, indicating a "single-state" picture, presumably the droplet model. Surprisingly, a single power law describes corrections to this result down to the smallest sizes studied.

D-Cysteine Ethyl Ester Reverses the Deleterious Effects of Morphine on Breathing and Arterial Blood-Gas Chemistry in Freely-Moving Rats

Cell-penetrant thiol esters including the disulfides, D-cystine diethyl ester and D-cystine dimethyl ester, and the monosulfide, L-glutathione ethyl ester, prevent and/or reverse the deleterious effects of opioids, such as morphine and fentanyl, on breathing and gas exchange within the lungs of unanesthetized/unrestrained rats without diminishing the antinociceptive or sedative effects of opioids. We describe here the effects of the monosulfide thiol ester, D-cysteine ethyl ester (D-CYSee), on intravenous morphine-induced changes in ventilatory parameters, arterial blood-gas chemistry, alveolar-arterial (A-a) gradient (i.e., index of gas exchange in the lungs), and sedation and antinociception in freely-moving rats. The bolus injection of morphine (10 mg/kg, IV) elicited deleterious effects on breathing, including depression of tidal volume, minute ventilation, peak inspiratory flow, and inspiratory drive. Subsequent injections of D-CYSee (2 × 500 μmol/kg, IV, given 15 min apart) elicited an immediate and sustained reversal of these effects of morphine. Morphine (10 mg/kg, IV) also A-a gradient, which caused a mismatch in ventilation perfusion within the lungs, and elicited pronounced changes in arterial blood-gas chemistry, including pronounced decreases in arterial blood pH, pO2 and sO2, and equally pronounced increases in pCO2 (all responses indicative of decreased ventilatory drive). These deleterious effects of morphine were immediately reversed by the injection of a single dose of D-CYSee (500 μmol/kg, IV). Importantly, the sedation and antinociception elicited by morphine (10 mg/kg, IV) were minimally affected by D-CYSee (500 μmol/kg, IV). In contrast, none of the effects of morphine were affected by administration of the parent thiol, D-cysteine (1 or 2 doses of 500 μmol/kg, IV). Taken together, these data suggest that D-CYSee may exert its beneficial effects via entry into cells that mediate the deleterious effects of opioids on breathing and gas exchange. Whether D-CYSee acts as a respiratory stimulant or counteracts the inhibitory actions of µ-opioid receptor activation remains to be determined. In conclusion, D-CYSee and related thiol esters may have clinical potential for the reversal of the adverse effects of opioids on breathing and gas exchange, while largely sparing antinociception and sedation.

Nontrivial maturation metastate-average state in a one-dimensional long-range Ising spin glass: Above and below the upper critical range

Understanding the low-temperature pure state structure of spin glasses remains an open problem in the field of statistical mechanics of disordered systems. Here we study Monte Carlo dynamics, performing simulations of the growth of correlations following a quench from infinite temperature to a temperature well below the spin-glass transition temperature T_{c} for a one-dimensional Ising spin-glass model with diluted long-range interactions. In this model, the probability P_{ij} that an edge {i,j} has nonvanishing interaction falls as a power law with chord distance, P_{ij}∝1/R_{ij}^{2σ}, and we study a range of values of σ with 1/2<σ<1. We consider a correlation function C_{4}(r,t). A dynamic correlation length that shows power-law growth with time ξ(t)∝t^{1/z} can be identified in the data and, for large time t, C_{4}(r,t) decays as a power law r^{-α_{d}} with distance r when r≪ξ(t). The calculation can be interpreted in terms of the maturation metastate averaged Gibbs state, or MMAS, and the decay exponent α_{d} differentiates between a trivial MMAS (α_{d}=0), as expected in the droplet picture of spin glasses, and a nontrivial MMAS (α_{d}≠0), as in the replica-symmetry-breaking (RSB) or chaotic pairs pictures. We find nonzero α_{d} even in the regime σ>2/3 which corresponds to short-range systems below six dimensions. For σ<2/3, the decay exponent α_{d} follows the RSB prediction for the decay exponent α_{s}=3-4σ of the static metastate, consistent with a conjectured statics-dynamics relation, while it approaches α_{d}=1-σ in the regime 2/3<σ<1; however, it deviates from both lines in the vicinity of σ=2/3.

Ordering behavior of the two-dimensional Ising spin glass with long-range correlated disorder

The standard short-range two-dimensional Ising spin glass is numerically well accessible, in particular, because there are polynomial-time ground-state algorithms. On the other hand, in contrast to higher dimensional spin glasses, it does not exhibit a rich behavior, i.e., no ordered phase at finite temperature. Here, we investigate whether long-range correlated bonds change this behavior. This would still keep the model numerically well accessible while exhibiting a more interesting behavior. The bonds are drawn from a Gaussian distribution with a two-point correlation for bonds at distance r that decays as (1+r^{2})^{-a/2}, a≥0. We study numerically with exact algorithms the ground-state and domain-wall excitations. Our results indicate that the inclusion of bond correlations still does not lead to a spin-glass order at any finite temperature. A further analysis reveals that bond correlations have a strong effect at local length scales, inducing ferro- and antiferromagnetic domains into the system. The length scale of ferro- and antiferromagnetic order diverges exponentially as the correlation exponent approaches a critical value, a→a_{crit}=0. Thus, our results suggest that the system becomes a ferro- or antiferromagnet only in the limit a→0.

D-Cystine di(m)ethyl ester reverses the deleterious effects of morphine on ventilation and arterial blood gas chemistry while promoting antinociception

We have identified thiolesters that reverse the negative effects of opioids on breathing without compromising antinociception. Here we report the effects of D-cystine diethyl ester (D-cystine diEE) or D-cystine dimethyl ester (D-cystine diME) on morphine-induced changes in ventilation, arterial-blood gas chemistry, A-a gradient (index of gas-exchange in the lungs) and antinociception in freely moving rats. Injection of morphine (10 mg/kg, IV) elicited negative effects on breathing (e.g., depression of tidal volume, minute ventilation, peak inspiratory flow, and inspiratory drive). Subsequent injection of D-cystine diEE (500 μmol/kg, IV) elicited an immediate and sustained reversal of these effects of morphine. Injection of morphine (10 mg/kg, IV) also elicited pronounced decreases in arterial blood pH, pO2 and sO2 accompanied by pronounced increases in pCO2 (all indicative of a decrease in ventilatory drive) and A-a gradient (mismatch in ventilation-perfusion in the lungs). These effects of morphine were reversed in an immediate and sustained fashion by D-cystine diME (500 μmol/kg, IV). Finally, the duration of morphine (5 and 10 mg/kg, IV) antinociception was augmented by D-cystine diEE. D-cystine diEE and D-cystine diME may be clinically useful agents that can effectively reverse the negative effects of morphine on breathing and gas-exchange in the lungs while promoting antinociception. Our study suggests that the D-cystine thiolesters are able to differentially modulate the intracellular signaling cascades that mediate morphine-induced ventilatory depression as opposed to those that mediate morphine-induced antinociception and sedation.

Percolation of Fortuin-Kasteleyn clusters for the random-bond Ising model

We apply generalizations of the Swendson-Wang and Wolff cluster algorithms, which are based on the construction of Fortuin-Kasteleyn clusters, to the three-dimensional ±1 random-bond Ising model. The behavior of the model is determined by the temperature T and the concentration p of negative (antiferromagnetic) bonds. The ground state is ferromagnetic for 0≤p<p_{c}, and a spin glass for p_{c}<p≤0.5 where p_{c}≃0.222. We investigate the percolation transition of the Fortuin-Kasteleyn clusters as a function of temperature for large system sizes up to N=200^{3} spins. Except for p=0 the Fortuin-Kasteleyn percolation transition occurs at a higher temperature than the magnetic ordering temperature. This was known before for p=1/2 but here we provide evidence for a difference in transition temperatures even for p arbitrarily small. Furthermore, for all values of p>0, our data suggest that the percolation transition is universal, irrespective of whether the ground state exhibits ferromagnetic or spin-glass order, and is in the universality class of standard percolation. This shows that correlations in the bond occupancy of the Fortuin-Kasteleyn clusters are irrelevant, except for p=0 where the clusters are strictly tied to Ising correlations so the percolation transition is in the Ising universality class.

Stability of the quantum Sherrington-Kirkpatrick spin glass model

I study in detail the quantum Sherrington-Kirkpatrick (SK) model, i.e., the infinite-range Ising spin glass in a transverse field, by solving numerically the effective one-dimensional model that the quantum SK model can be mapped to in the thermodynamic limit. I find that the replica symmetric solution is unstable down to zero temperature, in contrast to some previous claims, and so there is not only a line of transitions in the (longitudinal) field-temperature plane (the de Almeida-Thouless, AT, line) where replica symmetry is broken, but also a quantum de Almeida-Thouless (QuAT) line in the transverse field-longitudinal field plane at T=0. If the QuAT line also occurs in models with short-range interactions its presence might affect the performance of quantum annealers when solving spin glass-type problems with a bias (i.e., magnetic field).

Publisher's Note: Critical and Griffiths-McCoy singularities in quantum Ising spin glasses on d-dimensional hypercubic lattices: A series expansion study [Phys. Rev. E 96, 022139 (2017)]

This corrects the article DOI: 10.1103/PhysRevE.96.022139.

Critical and Griffiths-McCoy singularities in quantum Ising spin glasses on d-dimensional hypercubic lattices: A series expansion study

We study the ±J transverse-field Ising spin-glass model at zero temperature on d-dimensional hypercubic lattices and in the Sherrington-Kirkpatrick (SK) model, by series expansions around the strong-field limit. In the SK model and in high dimensions our calculated critical properties are in excellent agreement with the exact mean-field results, surprisingly even down to dimension d=6, which is below the upper critical dimension of d=8. In contrast, at lower dimensions we find a rich singular behavior consisting of critical and Griffiths-McCoy singularities. The divergence of the equal-time structure factor allows us to locate the critical coupling where the correlation length diverges, implying the onset of a thermodynamic phase transition. We find that the spin-glass susceptibility as well as various power moments of the local susceptibility become singular in the paramagnetic phase before the critical point. Griffiths-McCoy singularities are very strong in two dimensions but decrease rapidly as the dimension increases. We present evidence that high enough powers of the local susceptibility may become singular at the pure-system critical point.

de Almeida-Thouless instability in short-range Ising spin glasses

We use high-temperature series expansions to study the ±J Ising spin glass in a magnetic field in d-dimensional hypercubic lattices for d=5-8 and in the infinite-range Sherrington-Kirkpatrick (SK) model. The expansions are obtained in the variable w=tanh^{2}J/T for arbitrary values of u=tanh^{2}h/T complete to order w^{10}. We find that the scaling dimension Δ associated with the ordering-field h^{2} equals 2 in the SK model and for d≥6. However, in agreement with the work of Fisher and Sompolinsky [Phys. Rev. Lett. 54, 1063 (1985)PRLTAO0031-900710.1103/PhysRevLett.54.1063], there is a violation of scaling in a finite field, leading to an anomalous h-T dependence of the de Almeida-Thouless (AT) [J. Phys. A 11, 983 (1978)JPHAC50305-447010.1088/0305-4470/11/5/028] line in high dimensions, whereas scaling is restored as d→6. Within the convergence of our series analysis, we present evidence supporting an AT line in d≥6. In d=5, the exponents γ and Δ are substantially larger than mean-field values, but we do not see clear evidence for the AT line in d=5.

Spin glass behavior in a random Coulomb antiferromagnet

We study spin glass behavior in a random Ising Coulomb antiferromagnet in two and three dimensions using Monte Carlo simulations. In two dimensions, we find a transition at zero temperature with critical exponents consistent with those of the Edwards-Anderson model, though with large uncertainties. In three dimensions, evidence for a finite-temperature transition, as occurs in the Edwards-Anderson model, is rather weak. This may indicate that the sizes are too small to probe the asymptotic critical behavior, or possibly that the universality class is different from that of the Edwards-Anderson model and has a lower critical dimension equal to three.

Universal dynamic scaling in three-dimensional Ising spin glasses

We use a nonequilibrium Monte Carlo simulation method and dynamical scaling to study the phase transition in three-dimensional Ising spin glasses. The transition point is repeatedly approached at finite velocity v (temperature change versus time) in Monte Carlo simulations starting at a high temperature. This approach has the advantage that the equilibrium limit does not have to be strictly reached for a scaling analysis to yield critical exponents. For the dynamic exponent we obtain z=5.85(9) for bimodal couplings distribution and z=6.00(10) for the Gaussian case. Assuming universal dynamic scaling, we combine the two results and obtain z=5.93±0.07 for generic 3D Ising spin glasses.

Finite-size scaling above the upper critical dimension

We present a unified view of finite-size scaling (FSS) in dimension d above the upper critical dimension, for both free and periodic boundary conditions. We find that the modified FSS proposed some time ago to allow for violation of hyperscaling due to a dangerous irrelevant variable applies only to k=0 fluctuations, and "standard" FSS applies to k≠0 fluctuations. Hence the exponent η describing power-law decay of correlations at criticality is unambiguously η=0. With free boundary conditions, the finite-size "shift" is greater than the rounding. Nonetheless, using T-T(L), where T(L) is the finite-size pseudocritical temperature, rather than T-T(c), as the scaling variable, the data do collapse onto a scaling form that includes the behavior both at T(L), where the susceptibility χ diverges like L(d/2), and at the bulk T(c), where it diverges like L(2). These claims are supported by large-scale simulations on the five-dimensional Ising model.

Role of nitric oxide-containing factors in the ventilatory and cardiovascular responses elicited by hypoxic challenge in isoflurane-anesthetized rats

Exposure to hypoxia elicits changes in mean arterial blood pressure (MAP), heart rate, and frequency of breathing (fR). The objective of this study was to determine the role of nitric oxide (NO) in the cardiovascular and ventilatory responses elicited by brief exposures to hypoxia in isoflurane-anesthetized rats. The rats were instrumented to record MAP, heart rate, and fR and then exposed to 90 s episodes of hypoxia (10% O2, 90% N2) before and after injection of vehicle, the NO synthase inhibitor N(G)-nitro-L-arginine methyl ester (L-NAME), or the inactive enantiomer D-NAME (both at 50 μmol/kg iv). Each episode of hypoxia elicited a decrease in MAP, bidirectional changes in heart rate (initial increase and then a decrease), and an increase in fR. These responses were similar before and after injection of vehicle or D-NAME. In contrast, the hypoxia-induced decreases in MAP were attenuated after administration of L-NAME. The initial increases in heart rate during hypoxia were amplified whereas the subsequent decreases in heart rate were attenuated in L-NAME-treated rats. Finally, the hypoxia-induced increases in fR were virtually identical before and after administration of L-NAME. These findings suggest that NO factors play a vital role in the expression of the cardiovascular but not the ventilatory responses elicited by brief episodes of hypoxia in isoflurane-anesthetized rats. Based on existing evidence that NO factors play a vital role in carotid body and central responses to hypoxia in conscious rats, our findings raise the novel possibility that isoflurane blunts this NO-dependent signaling.

Role of central and peripheral opiate receptors in the effects of fentanyl on analgesia, ventilation and arterial blood-gas chemistry in conscious rats

This study determined the effects of the peripherally restricted μ-opiate receptor (μ-OR) antagonist, naloxone methiodide (NLXmi) on fentanyl (25μg/kg, i.v.)-induced changes in (1) analgesia, (2) arterial blood gas chemistry (ABG) and alveolar-arterial gradient (A-a gradient), and (3) ventilatory parameters, in conscious rats. The fentanyl-induced increase in analgesia was minimally affected by a 1.5mg/kg of NLXmi but was attenuated by a 5.0mg/kg dose. Fentanyl decreased arterial blood pH, pO2 and sO2 and increased pCO2 and A-a gradient. These responses were markedly diminished in NLXmi (1.5mg/kg)-pretreated rats. Fentanyl caused ventilatory depression (e.g., decreases in tidal volume and peak inspiratory flow). Pretreatment with NLXmi (1.5mg/kg, i.v.) antagonized the fentanyl decrease in tidal volume but minimally affected the other responses. These findings suggest that (1) the analgesia and ventilatory depression caused by fentanyl involve peripheral μ-ORs and (2) NLXmi prevents the fentanyl effects on ABG by blocking the negative actions of the opioid on tidal volume and A-a gradient.

L-Cysteine ethyl ester reverses the deleterious effects of morphine on, arterial blood-gas chemistry in tracheotomized rats

This study determined whether the membrane-permeable ventilatory stimulant, L-cysteine ethylester (L-CYSee), reversed the deleterious actions of morphine on arterial blood-gas chemistry in isoflurane-anesthetized rats. Morphine (2 mg/kg, i.v.) elicited sustained decreases in arterial blood pH, pO₂ and sO₂, and increases in pCO₂ (all responses indicative of hypoventilation) and alveolar-arterial gradient (indicative of ventilation-perfusion mismatch). Injections of L-CYSee (100 μmol/kg, i.v.) reversed the effects of morphine in tracheotomized rats but were minimally active in non-tracheotomized rats. L-cysteine or L-serine ethylester (100 μmol/kg, i.v.) were without effect. It is evident that L-CYSee can reverse the negative effects of morphine on arterial blood-gas chemistry and alveolar-arterial gradient but that this positive activity is negated by increases in upper-airway resistance. Since L-cysteine and L-serine ethylester were ineffective, it is evident that cell penetrability and the sulfur moiety of L-CYSee are essential for activity. Due to its ready penetrability into the lungs, chest wall muscle and brain, the effects of L-CYSee on morphine-induced changes in arterial blood-gas chemistry are likely to involve both central and peripheral sites of action.

Low-dose morphine elicits ventilatory excitant and depressant responses in conscious rats: Role of peripheral μ-opioid receptors

The systemic administration of morphine affects ventilation via a mixture of central and peripheral actions. The aims of this study were to characterize the ventilatory responses elicited by a low dose of morphine in conscious rats; to determine whether tolerance develops to these responses; and to determine the potential roles of peripheral μ-opioid receptors (μ-ORs) in these responses. Ventilatory parameters were monitored via unrestrained whole-body plethysmography. Conscious male Sprague-Dawley rats received an intravenous injection of vehicle or the peripherally-restricted μ-OR antagonist, naloxone methiodide (NLXmi), and then three successive injections of morphine (1 mg/kg) given 30 min apart. The first injection of morphine in vehicle-treated rats elicited an array of ventilatory excitant (i.e., increases in frequency of breathing, minute volume, respiratory drive, peak inspiratory and expiratory flows, accompanied by decreases in inspiratory time and end inspiratory pause) and inhibitory (i.e., a decrease in tidal volume and an increase in expiratory time) responses. Subsequent injections of morphine elicited progressively and substantially smaller responses. The pattern of ventilatory responses elicited by the first injection of morphine was substantially affected by pretreatment with NLXmi whereas NLXmi minimally affected the development of tolerance to these responses. Low-dose morphine elicits an array of ventilatory excitant and depressant effects in conscious rats that are subject to the development of tolerance. Many of these initial actions of morphine appear to involve activation of peripheral μ-ORs whereas the development of tolerance to these responses does not.

Morphine has latent deleterious effects on the ventilatory responses to a hypoxic-hypercapnic challenge

This study explored the concept that morphine has latent deleterious actions on the ventilatory control systems that respond to a hypoxic-hypercapnic challenge. In this study, we examined the ventilatory responses elicited by hypoxic-hypercapnic challenge in conscious rats at a time when the effects of morphine (10 mg/kg) on arterial blood-gas chemistry and minute ventilation had subsided. Morphine induced pronounced changes in arterial blood-gas chemistry (e.g., an increase in pCO₂, decreases in pO₂ and sO₂) and decreases in minute ventilation. Despite the complete resolution of the morphine-induced changes in arterial blood-gas chemistry and minute ventilation and almost complete resolution of the effects on peak inspiratory flow and peak expiratory flow, subsequent exposure to hypoxic-hypercapnic challenge elicited markedly blunted increases in minute ventilation and in peak inspiratory and expiratory flows. These findings demonstrate that (1) the changes in arterial blood-gas chemistry elicited by morphine parallel changes in minute ventilation rather than PIF and PEF, and (2) morphine has latent untoward effects on the ventilatory responses to hypoxic-hypercapnic challenge. These novel findings raise the possibility that patients deemed to have recovered from the acute ventilatory depressant effects of morphine may still be susceptible to the latent effects of this opioid analgesic. The mechanisms underlying these latent effects remain to be elucidated.

Spin glasses in the nonextensive regime

Spin systems with long-range interactions are "nonextensive" if the strength of the interactions falls off sufficiently slowly with distance. It has been conjectured for ferromagnets and, more recently, for spin glasses that, everywhere in the nonextensive regime, the free energy is exactly equal to that for the infinite range model in which the characteristic strength of the interaction is independent of distance. In this paper we present the results of Monte Carlo simulations of the one-dimensional long-range spin glasses in the nonextensive regime. Using finite-size scaling, our results for the transition temperatures are consistent with this prediction. We also propose and provide numerical evidence for an analogous result for dilutedlong-range spin glasses in which the coordination number is finite, namely, that the transition temperature throughout the nonextensive regime is equal to that of the infinite-range model known as the Viana-Bray model.

Exponential complexity of the quantum adiabatic algorithm for certain satisfiability problems

We determine the complexity of several constraint satisfaction problems using the quantum adiabatic algorithm in its simplest implementation. We do so by studying the size dependence of the gap to the first excited state of "typical" instances. We find that, at large sizes N, the complexity increases exponentially for all models that we study. We also compare our results against the complexity of the analogous classical algorithm WalkSAT and show that the harder the problem is for the classical algorithm, the harder it is also for the quantum adiabatic algorithm.

Complexity of several constraint-satisfaction problems using the heuristic classical algorithm WalkSAT

We determine the complexity of several constraint-satisfaction problems using the heuristic algorithm WalkSAT. At large sizes N, the complexity increases exponentially with N in all cases. Perhaps surprisingly, out of all the models studied, the hardest for WalkSAT is the one for which there is a polynomial time algorithm.

de Almeida-Thouless line in vector spin glasses

We consider the infinite-range spin glass in which the spins have m>1 components (a vector spin glass). Applying a magnetic field which is random in direction, there is a de Almeida-Thouless (AT) line below which the "replica symmetric" solution is unstable, just as for the Ising (m=1) case. We calculate the location of this AT line for Gaussian random fields for arbitrary m and verify our results by numerical simulations for m=3 .

First-order phase transition in the quantum adiabatic algorithm

We simulate the quantum adiabatic algorithm (QAA) for the exact cover problem for sizes up to N=256 using quantum Monte Carlo simulations incorporating parallel tempering. At large N, we find that some instances have a discontinuous (first-order) quantum phase transition during the evolution of the QAA. This fraction increases with increasing N and may tend to 1 for N-->infinity.

Continuum and lattice heat currents for oscillator chains

We show that two commonly used definitions for the heat current give different results-through the Kubo formula-for the heat conductivity of oscillator chains. The difference exists for finite chains, and is expected to be important more generally for small structures. For a chain of N particles that are tethered at the ends, the ratio of the heat conductivities calculated with the two currents differs from unity by O(1/N). For a chain held at constant pressure, the difference from unity decays more slowly, and is consistent with O(1/Neta) with 1>eta>0.5.

Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses

We test for the existence of a spin-glass phase transition, the de Almeida-Thouless line, in an externally applied (random) magnetic field by performing Monte Carlo simulations on a power-law diluted one-dimensional Ising spin glass for very large system sizes. We find that a de Almeida-Thouless line occurs only in the mean-field regime, which corresponds, for a short-range spin glass, to dimension d larger than 6.

Size dependence of the minimum excitation gap in the quantum adiabatic algorithm

We study the typical (median) value of the minimum gap in the quantum version of the exact cover problem using quantum Monte Carlo simulations, in order to understand the complexity of the quantum adiabatic algorithm for much larger sizes than before. For a range of sizes N< or =128, where the classical Davis-Putnam algorithm shows exponential median complexity, the quantum adiabatic algorithm shows polynomial median complexity. The bottleneck of the algorithm is an isolated avoided-crossing point of a Landau-Zener type (collision between the two lowest energy levels only).

Defect energy of infinite-component vector spin glasses

We compute numerically the zero-temperature defect energy DeltaE of the vector spin glass in the limit of an infinite number of spin components m , for a range of dimensions 2< or d < or =5 . Fitting to DeltaE approximately L(theta) , where L is the system size, we obtain: theta similar to-1.54 (d=2) , theta similar to-1.04 (d=3) , theta similar to -0.67 (d=4) , and theta similar to -0.37 (d=5) . These results show that the lower critical dimension dl (the dimension where theta changes sign) is significantly higher for m=infinity than for finite m (where 2< dl <3 ).

Spin glasses in the limit of an infinite number of spin components

We consider spin glass models in which the number of spin components m is infinite. In the formulation of the problem appropriate for numerical calculations proposed by several authors, we show that the order parameter defined by the long-distance limit of the correlation functions is actually zero and there is only "quasi-long-range order" below the transition temperature. Nonetheless, there can be a finite temperature phase transition where the decay of correlations changes from exponential to power law. We also show that the spin glass transition temperature is zero in three dimensions so power-law behavior only occurs at T=0 in this case. We also argue that the order of limits, m-->infinity and N-->infinity is important, where N is the number of spins.

Phase transition in vector spin glasses

We first give an experimental and theoretical introduction to spin glasses, and then discuss the nature of the phase transition in spin glasses with vector spins. Results of Monte Carlo simulations of the Heisenberg spin glass model in three dimensions are presented. A finite size scaling analysis of the correlation length of the spins and chiralities shows that there is a single, finite-temperature transition at which both spins and chiralities order.

Absence of an Almeida-Thouless line in three-dimensional spin glasses

We present results of Monte Carlo simulations of the three-dimensional Edwards-Anderson Ising spin glass in the presence of a (random) field. A finite-size scaling analysis of the correlation length shows no indication of a transition, in contrast with the zero-field case. This suggests that there is no Almeida-Thouless line for short-range Ising spin glasses.

Lack of ultrametricity in the low-temperature phase of three-dimensional Ising spin glasses

We study the low-temperature spin-glass phases of the Sherrington-Kirkpatrick (SK) model and of the 3-dimensional short-range Ising spin-glass (3DISG). By using clustering to focus on the relevant parts of phase space and reduce finite size effects, we found that for the SK model ultrametricity becomes clearer as the system size increases, while for the short-range case our results indicate the opposite, i.e., lack of ultrametricity. Another method, which does not rely on clustering, indicates that the mean-field solution works for the SK model but does not apply in detail to the 3DISG, for which stochastic stability is also violated.

Single spin and chiral glass transition in vector spin glasses in three dimensions

Results of Monte Carlo simulations of XY and Heisenberg spin glass models in three dimensions are presented. A finite-size scaling analysis of the correlation length of the spins and chiralities of both models shows that there is a single, finite-temperature transition at which both spins and chiralities order.

Interface energies in ising spin glasses

The replica method has been used to calculate the interface free energy associated with the change from periodic to antiperiodic boundary conditions in finite-dimensional spin glasses. At mean-field level the interface free energy vanishes, but after allowing for fluctuation effects, a nonzero interface free energy is obtained which is significantly different from numerical expectations.

Convergence of Monte Carlo simulations to equilibrium

We give two direct, elementary proofs that a Monte Carlo simulation converges to equilibrium provided that appropriate conditions are satisfied. The first proof requires detailed balance while the second is quite general.

Therapeutic implications of human endothelial nitric oxide synthase gene polymorphism

Vascular endothelial dysfunction is now recognized as a common phenomenon in an array of cardiovascular disorders. Production of nitric oxide via the endothelial isoform of nitric oxide synthase [eNOS (previously termed NOS3 or ecNOS)] is vital for a healthy endothelium; several polymorphic variations of the gene encoding eNOS (NOS3) are now known and have been investigated with respect to disease risk. Surprisingly, only approximately half of these studies have demonstrated significant associations between NOS3 polymorphisms and cardiovascular disease, and many reports are contradictory. Central issues include adequate statistical power, appropriateness of control cohorts, multigene interactions and plausible biological consequences. So far, the inconsistencies are not unique to the NOS3 polymorphisms, but probably represent the broad challenges in defining genetic aspects of complex disease processes.