Critical Exponents from General Distributions of Zeroes

All of the thermodynamic information on a statistical mechanical system is encoded in the locus and density of its partition function zeroes. Recently, a new technique was developed which enables the extraction of the latter using finite-size data of the type typically garnered from a computational approach. Here that method is extended to deal with more general cases. Other critical points of a type which appear in many models are also studied.Comment: 4 pages, 3 figure

New methods to measure phase transition strength

A recently developed technique to determine the order and strength of phase transitions by extracting the density of partition function zeroes (a continuous function) from finite-size systems (a discrete data set) is generalized to systems for which (i) some or all of the zeroes occur in degenerate sets and/or (ii) they are not confined to a singular line in the complex plane. The technique is demonstrated by application to the case of free Wilson fermions.Comment: 3 pages, 2 figures, Lattice2002(spin

Glassy transition and metastability in four-spin Ising model

Using Monte Carlo simulations we show that the three-dimensional Ising model with four-spin (plaquette) interactions has some characteristic glassy features. The model dynamically generates diverging energy barriers, which give rise to slow dynamics at low temperature. Moreover, in a certain temperature range the model possesses a metastable (supercooled liquid) phase, which is presumably supported by certain entropy barriers. Although extremely strong, metastability in our model is only a finite-size effect and sufficiently large droplets of stable phase divert evolution of the system toward the stable phase. Thus, the glassy transitions in this model is a dynamic transition, preceded by a pronounced peak in the specific heat.Comment: extensively revised, with further simulations of metastability properties, response to referees tactfully remove

Condensation in the Backgammon model

We analyse the properties of a very simple ``balls-in-boxes'' model which can exhibit a phase transition between a fluid and a condensed phase, similar to behaviour encountered in models of random geometries in one, two and four dimensions. This model can be viewed as a generalisation of the backgammon model introduced by Ritort as an example of glassy behaviour without disorder.Comment: 14 pages, requires Latex2e + elsart.cls (supplied). 2 figures included as eps files. (some minor errors had been corrected and additional references added

Calculation of the singlet-triplet gap of the antiferromagnetic Heisenberg Model on the ladder

The ground state energy and the singlet-triplet energy gap of the antiferromagnetic Heisenberg model on a ladder is investigated using a mean field theory and the density matrix renormalization group. Spin wave theory shows that the corrections to the local magnetization are infinite. This indicates that no long range order occurs in this system. A flux-phase state is used to calculate the energy gap as a function of the transverse coupling, $J_\perp$, in the ladder. It is found that the gap is linear in $J_\perp$ for $J_\perp\gg 1$ and goes to zero for $J_\perp\to 0$. The mean field theory agrees well with the numerical results.Comment: 11pages,6 figures (upon request) Revtex 3.0, Report#CRPS-94-0

Thermodynamic Properties and Elementary Excitations in Quantum Sine-Gordon Spin System KCuGaF6

Thermodynamic properties and elementary excitations in $S=1/2$ one-dimensional Heisenberg antiferromagnet KCuGaF$_6$ were investigated by magnetic susceptibility, specific heat and ESR measurements. Due to the Dzyaloshinsky-Moriya interaction with alternating $D$-vectors and/or the staggered $g$-tensor, the staggered magnetic field is induced when subjected to external magnetic field. Specific heat in magnetic field clearly shows the formation of excitation gap, which is attributed to the staggered magnetic field. The specific heat data was analyzed on the basis of the quantum sine-Gordon (SG) model. We observed many ESR modes including one soliton and three breather excitations characteristic of the quantum SG model.Comment: 4 pages, 5 figures, to appear in J. Phys. Soc. Jpn., vol. 76, no.

Thermodynamics of Spin S = 1/2 Antiferromagnetic Uniform and Alternating-Exchange Heisenberg Chains

The magnetic susceptibility chi and specific heat C versus temperature T of the spin-1/2 antiferromagnetic alternating-exchange (J1 and J2) Heisenberg chain are studied for the entire range 0 \leq alpha \leq 1 of the alternation parameter alpha = J2/J1. For the uniform chain (alpha = 1), detailed comparisons of the high-accuracy chi(T) and C(T) Bethe ansatz data of Kluemper and Johnston are made with the asymptotically exact low-T field theory predictions of Lukyanov. QMC simulations and TMRG calculations of chi(alpha,T) are presented. From the low-T TMRG data, the spin gap Delta(alpha)/J1 is extracted for 0.8 \leq alpha \leq 0.995. High accuracy fits to all of the above numerical data are obtained. We examine in detail the theoretical predictions of Bulaevskii for chi(alpha,T) and compare them with our results. Our experimental chi(T) and C(T) data for NaV2O5 single crystals are modeled in detail. The chi(T) data above the spin dimerization temperature Tc = 34 K are not in agreement with the prediction for the uniform Heisenberg chain, but can be explained if there is a moderate ferromagnetic interchain coupling and/or if J changes with T. By fitting the chi(T) data, we obtain Delta(T = 0) = 103(2) K, alternation parameter delta(0) = (1 - alpha)/(1 + alpha) = 0.034(6) and average exchange constant J(0) = 640(80) K. The delta(T) and Delta(T) are derived from the data. A spin pseudogap with a large magnitude \approx 0.4 Delta(0) is consistently found just above Tc, which decreases with increasing T. Analysis of our C(T) data indicates that at Tc, at least 77% of the entropy change due to the transition at Tc and associated order parameter fluctuations arise from the lattice and/or charge degrees of freedom and less than 23% from the spin degrees of freedom.Comment: 53 two-column REVTeX pages, 50 embedded figures, 7 tables. Revisions required due to incorrect Eq. (39) in Ref. 51 which gives the low-T approximation for the specific heat of a S = 1/2 1D system with a spin gap; no conclusions were changed. Additional minor revisions made. Phys. Rev. B (in press

Dynamic redox conditions control late Ediacaran metazoan ecosystems in the Nama Group, Namibia

The first appearance of skeletal metazoans in the late Ediacaran (~550 million years ago; Ma) has been linked to the widespread development of oxygenated oceanic conditions, but a precise spatial and temporal reconstruction of their evolution has not been resolved. Here we consider the evolution of ocean chemistry from ~550 to ~541. Ma across shelf-to-basin transects in the Zaris and Witputs Sub-Basins of the Nama Group, Namibia. New carbon isotope data capture the final stages of the Shuram/Wonoka deep negative C-isotope excursion, and these are complemented with a reconstruction of water column redox dynamics utilising Fe-S-C systematics and the distribution of skeletal and soft-bodied metazoans. Combined, these inter-basinal datasets provide insight into the potential role of ocean redox chemistry during this pivotal interval of major biological innovation.The strongly negative δ13C values in the lower parts of the sections reflect both a secular, global change in the C-isotopic composition of Ediacaran seawater, as well as the influence of 'local' basinal effects as shown by the most negative δ13C values occurring in the transition from distal to proximal ramp settings. Critical, though, is that the transition to positive δ13C values postdates the appearance of calcified metazoans, indicating that the onset of biomineralization did not occur under post-excursion conditions.Significantly, we find that anoxic and ferruginous deeper water column conditions were prevalent during and after the transition to positive δ13C that marks the end of the Shuram/Wonoka excursion. Thus, if the C isotope trend reflects the transition to global-scale oxygenation in the aftermath of the oxidation of a large-scale, isotopically light organic carbon pool, it was not sufficient to fully oxygenate the deep ocean.Both sub-basins reveal highly dynamic redox structures, where shallow, inner ramp settings experienced transient oxygenation. Anoxic conditions were caused either by episodic upwelling of deeper anoxic waters or higher rates of productivity. These settings supported short-lived and monospecific skeletal metazoan communities. By contrast, microbial (thrombolite) reefs, found in deeper inner- and mid-ramp settings, supported more biodiverse communities with complex ecologies and large skeletal metazoans. These long-lived reef communities, as well as Ediacaran soft-bodied biotas, are found particularly within transgressive systems, where oxygenation was persistent. We suggest that a mid-ramp position enabled physical ventilation mechanisms for shallow water column oxygenation to operate during flooding and transgressive sea-level rise. Our data support a prominent role for oxygen, and for stable oxygenated conditions in particular, in controlling both the distribution and ecology of Ediacaran skeletal metazoan communities

Patterns of HIV prevalence among injecting drug users in the cross-border area of Lang Son Province, Vietnam, and Ning Ming County, Guangxi Province, China

BACKGROUND: To assess patterns of injecting drug use and HIV prevalence among injecting drug users (IDUs) in an international border area along a major heroin trans-shipment route. METHODS: Cross-sectional surveys of IDUs in 5 sites in Lang Son Province, Vietnam (n = 348) and 3 sites in Ning Ming County, Guangxi Province, China (n = 308). Respondents were recruited through peer referral ("snowball") methods in both countries, and also from officially recorded lists of IDUs in Vietnam. A risk behavior questionnaire was administered and HIV counseling and testing conducted. RESULTS: Participants in both countries were largely male, in their 20s, and unmarried. A majority of subjects in both countries were members of ethnic minority groups. There were strong geographic gradients for length of drug injecting and for HIV seroprevalence. Both mean years injecting and HIV seroprevalence declined from the Vietnamese site farthest from the border to the Chinese site farthest from the border. 10.6% of participants in China and 24.5% of participants in Vietnam reported crossing the international border in the 6 months prior to interview. Crossing the border by IDUs was associated with (1) distance from the border, (2) being a member of an ethnic minority group, and (3) being HIV seropositive among Chinese participants. CONCLUSION: Reducing the international spread of HIV among IDUs will require programs at the global, regional, national, and "local cross border" levels. At the local cross border level, the programs should be coordinated on both sides of the border and on a sufficient scale that IDUs will be able to readily obtain clean injection equipment on the other side of the border as well as in their country of residence

Comparing Respondent-Driven Sampling and Targeted Sampling Methods of Recruiting Injection Drug Users in San Francisco

The objective of this article is to compare demographic characteristics, risk behaviors, and service utilization among injection drug users (IDUs) recruited from two separate studies in San Francisco in 2005, one which used targeted sampling (TS) and the other which used respondent-driven sampling (RDS). IDUs were recruited using TS (n = 651) and RDS (n = 534) and participated in quantitative interviews that included demographic characteristics, risk behaviors, and service utilization. Prevalence estimates and 95% confidence intervals (CIs) were calculated to assess whether there were differences in these variables by sampling method. There was overlap in 95% CIs for all demographic variables except African American race (TS: 45%, 53%; RDS: 29%, 44%). Maps showed that the proportion of IDUs distributed across zip codes were similar for the TS and RDS sample, with the exception of a single zip code that was more represented in the TS sample. This zip code includes an isolated, predominantly African American neighborhood where only the TS study had a field site. Risk behavior estimates were similar for both TS and RDS samples, although self-reported hepatitis C infection was lower in the RDS sample. In terms of service utilization, more IDUs in the RDS sample reported no recent use of drug treatment and syringe exchange program services. Our study suggests that perhaps a hybrid sampling plan is best suited for recruiting IDUs in San Francisco, whereby the more intensive ethnographic and secondary analysis components of TS would aid in the planning of seed placement and field locations for RDS