Metastability in the dilute Ising model

Consider Glauber dynamics for the Ising model on the hypercubic lattice with a positive magnetic field. Starting from the minus configuration, the system initially settles into a metastable state with negative magnetization. Slowly the system relaxes to a stable state with positive magnetization. Schonmann and Shlosman showed that in the two dimensional case the relaxation time is a simple function of the energy required to create a critical Wulff droplet. The dilute Ising model is obtained from the regular Ising model by deleting a fraction of the edges of the underlying graph. In this paper we show that even an arbitrarily small dilution can dramatically reduce the relaxation time. This is because of a catalyst effect---rare regions of high dilution speed up the transition from minus phase to plus phase.Comment: 49 page

Nature vs. Nurture: Dynamical Evolution in Disordered Ising Ferromagnets

We study the predictability of zero-temperature Glauber dynamics in various models of disordered ferromagnets. This is analyzed using two independent dynamical realizations with the same random initialization (called twins). We derive, theoretically and numerically, trajectories for the evolution of the normalized magnetization and twin overlap as the system size tends to infinity. The systems we treat include mean-field ferromagnets with light-tailed and heavy-tailed coupling distributions, as well as highly-disordered models with a variety of other geometries. In the mean-field setting with light-tailed couplings, the disorder averages out and the limiting trajectories of the magnetization and twin overlap match those of the homogenous Curie--Weiss model. On the other hand, when the coupling distribution has heavy tails, or the geometry changes, the effect of the disorder persists in the thermodynamic limit. Nonetheless, qualitatively all such random ferromagnets share a similar time evolution for their twin overlap, wherein the two twins initially decorrelate, before either partially or fully converging back together due to the ferromagnetic drift.Comment: 16 pages, 7 figure

Dynamical frustration in ANNNI model and annealing

Zero temperature quench in the Axial Next Nearest Neighbour Ising (ANNNI) model fails to bring it to its ground state for a certain range of values of the frustration parameter $\kappa$, the ratio of the next nearest neighbour antiferromagnetic interaction strength to the nearest neighbour one. We apply several annealing methods, both classical and quantum, and observe that the behaviour of the residual energy and the order parameter depends on the value of $\kappa$ strongly. Classical or thermal annealing is found to be adequate for small values of $\kappa$. However, neither classical nor quantum annealing is effective at values of $\kappa$ close to the fully frustrated point $\kappa=0.5$, where the residual energy shows a very slow algebraic decay with the number of MCS.Comment: 6 pages,10 figures, to be published in Proceedings of " The International Workshop on Quantum annealing and other Optimization Methods

Cluster Monte Carlo study of multi-component fluids of the Stillinger-Helfand and Widom-Rowlinson type

Phase transitions of fluid mixtures of the type introduced by Stillinger and Helfand are studied using a continuum version of the invaded cluster algorithm. Particles of the same species do not interact, but particles of different types interact with each other via a repulsive potential. Examples of interactions include the Gaussian molecule potential and a repulsive step potential. Accurate values of the critical density, fugacity and magnetic exponent are found in two and three dimensions for the two-species model. The effect of varying the number of species and of introducing quenched impurities is also investigated. In all the cases studied, mixtures of $q$-species are found to have properties similar to $q$-state Potts models.Comment: 25 pages, 5 figure

PROMIS 4-item measures and numeric rating scales efficiently assess SPADE symptoms compared with legacy measures

Objective The 5 SPADE (sleep, pain, anxiety, depression, and low energy/fatigue) symptoms are among the most prevalent and disabling symptoms in clinical practice. This study evaluates the minimally important difference (MID) of Patient-Reported Outcomes Measurement Information System (PROMIS) measures and their correspondence with other brief measures to assess SPADE symptoms. Study Design and Setting Three hundred primary care patients completed a 4-item PROMIS scale, a numeric rating scale (NRS), and a non-PROMIS legacy scale for each of the 5 SPADE symptoms. Optimal NRS cutpoints were examined, and cross-walk units for converting legacy measure scores to PROMIS scores were determined. PROMIS scores corresponding to standard deviation (SD) and standard error of measurement (SEM) changes in legacy scores were used to estimate MID. Results At an NRS ≥5, the mean PROMIS T-score exceeded 55 (the operational threshold for a clinically meaningful symptom) for each SPADE symptom. Correlations were high (0.70–0.86) between each PROMIS scale and its corresponding non-PROMIS legacy scale. Changes in non-PROMIS legacy scale scores of 0.35 SD and 1 SEM corresponded to mean PROMIS T-scores of 2.92 and 3.05 across the 5 SPADE symptoms, with changes in 0.2 and 0.5 SD corresponding to mean PROMIS T-scores of 1.67 and 4.16. Conclusion A 2-step screening process for SPADE symptoms might use single-item NRS scores, proceeding to PROMIS scales for NRS scores ≥5. A PROMIS T-score change of three points represents a reasonable MID estimate, with two to four points approximating lower and upper bounds

Longitudinal Analysis of Quality of Life, Clinical, Radiographic, Echocardiographic, and Laboratory Variables in Dogs with Myxomatous Mitral Valve Disease Receiving Pimobendan or Benazepril: The QUEST Study

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