Model C critical dynamics of random anisotropy magnets

We study the relaxational critical dynamics of the three-dimensional random anisotropy magnets with the non-conserved n-component order parameter coupled to a conserved scalar density. In the random anisotropy magnets the structural disorder is present in a form of local quenched anisotropy axes of random orientation. When the anisotropy axes are randomly distributed along the edges of the n-dimensional hypercube, asymptotical dynamical critical properties coincide with those of the random-site Ising model. However structural disorder gives rise to considerable effects for non-asymptotic critical dynamics. We investigate this phenomenon by a field-theoretical renormalization group analysis in the two-loop order. We study critical slowing down and obtain quantitative estimates for the effective and asymptotic critical exponents of the order parameter and scalar density. The results predict complex scenarios for the effective critical exponent approaching an asymptotic regime.Comment: 8 figures, style files include

Deciding Entailments in Inductive Separation Logic with Tree Automata

Separation Logic (SL) with inductive definitions is a natural formalism for specifying complex recursive data structures, used in compositional verification of programs manipulating such structures. The key ingredient of any automated verification procedure based on SL is the decidability of the entailment problem. In this work, we reduce the entailment problem for a non-trivial subset of SL describing trees (and beyond) to the language inclusion of tree automata (TA). Our reduction provides tight complexity bounds for the problem and shows that entailment in our fragment is EXPTIME-complete. For practical purposes, we leverage from recent advances in automata theory, such as inclusion checking for non-deterministic TA avoiding explicit determinization. We implemented our method and present promising preliminary experimental results

The Tree Width of Separation Logic with Recursive Definitions

Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current results report on techniques to decide satisfiability and validity of entailments for Separation Logic(s) over lists (possibly with data). In this paper we establish a more general decidability result. We prove that any Separation Logic formula using rather general recursively defined predicates is decidable for satisfiability, and moreover, entailments between such formulae are decidable for validity. These predicates are general enough to define (doubly-) linked lists, trees, and structures more general than trees, such as trees whose leaves are chained in a list. The decidability proofs are by reduction to decidability of Monadic Second Order Logic on graphs with bounded tree width.Comment: 30 pages, 2 figure

Zero-temperature behavior of the random-anisotropy model in the strong-anisotropy limit

We consider the random-anisotropy model on the square and on the cubic lattice in the strong-anisotropy limit. We compute exact ground-state configurations, and we use them to determine the stiffness exponent at zero temperature; we find $\theta = -0.275(5)$ and $\theta \approx 0.2$ respectively in two and three dimensions. These results show that the low-temperature phase of the model is the same as that of the usual Ising spin-glass model. We also show that no magnetic order occurs in two dimensions, since the expectation value of the magnetization is zero and spatial correlation functions decay exponentially. In three dimensions our data strongly support the absence of spontaneous magnetization in the infinite-volume limit

Universality classes of three-dimensional mnmn-vector model

We study the conditions under which the critical behavior of the three-dimensional $mn$-vector model does not belong to the spherically symmetrical universality class. In the calculations we rely on the field-theoretical renormalization group approach in different regularization schemes adjusted by resummation and extended analysis of the series for renormalization-group functions which are known for the model in high orders of perturbation theory. The phase diagram of the three-dimensional $mn$-vector model is built marking out domains in the $mn$-plane where the model belongs to a given universality class.Comment: 9 pages, 1 figur

Harmonic crossover exponents in O(n) models with the pseudo-epsilon expansion approach

We determine the crossover exponents associated with the traceless tensorial quadratic field, the third- and fourth-harmonic operators for O(n) vector models by re-analyzing the existing six-loop fixed dimension series with pseudo-epsilon expansion. Within this approach we obtain the most accurate theoretical estimates that are in optimum agreement with other theoretical and experimental results.Comment: 12 pages, 1 figure. Final version accepted for publicatio

Predicate Abstraction for Linked Data Structures

We present Alias Refinement Types (ART), a new approach to the verification of correctness properties of linked data structures. While there are many techniques for checking that a heap-manipulating program adheres to its specification, they often require that the programmer annotate the behavior of each procedure, for example, in the form of loop invariants and pre- and post-conditions. Predicate abstraction would be an attractive abstract domain for performing invariant inference, existing techniques are not able to reason about the heap with enough precision to verify functional properties of data structure manipulating programs. In this paper, we propose a technique that lifts predicate abstraction to the heap by factoring the analysis of data structures into two orthogonal components: (1) Alias Types, which reason about the physical shape of heap structures, and (2) Refinement Types, which use simple predicates from an SMT decidable theory to capture the logical or semantic properties of the structures. We prove ART sound by translating types into separation logic assertions, thus translating typing derivations in ART into separation logic proofs. We evaluate ART by implementing a tool that performs type inference for an imperative language, and empirically show, using a suite of data-structure benchmarks, that ART requires only 21% of the annotations needed by other state-of-the-art verification techniques

Early postnatal development of the lumbar vertebrae in male Wistar rats: double staining and digital radiological studies

The aim of the study was to evaluate the physiological developmental changes of male rats’ lumbar vertebrae during the first 22 days after birth. Morphology and mineralisation of lumbar vertebrae were evaluated using double-staining and digital radiography system, which allowed vertebral width and optical density to be determined. Pup weight, crown-rump length, body mass index and vertebral width increased during postnatal period and significantly correlated with their age. Bone mineralisation, as measured by optical density, did not show any significant differences. The complete fusion of the primary ossification centres had a cranio- -caudal direction and started on day 19 after parturition but was incomplete by day 22. It could be concluded that, unlike significant age-related increase of vertebral size, mineralisation was only slightly elevated during evaluated postnatal period. The method described is supplementary to alizarin red S staining as it provides both qualitative and quantitative data on mineralisation in a similar manner to micro computed tomography but does not allow 3 dimensional and microarchitecture examination

Critical behavior of the random-anisotropy model in the strong-anisotropy limit

We investigate the nature of the critical behavior of the random-anisotropy Heisenberg model (RAM), which describes a magnetic system with random uniaxial single-site anisotropy, such as some amorphous alloys of rare earths and transition metals. In particular, we consider the strong-anisotropy limit (SRAM), in which the Hamiltonian can be rewritten as the one of an Ising spin-glass model with correlated bond disorder. We perform Monte Carlo simulations of the SRAM on simple cubic L^3 lattices, up to L=30, measuring correlation functions of the replica-replica overlap, which is the order parameter at a glass transition. The corresponding results show critical behavior and finite-size scaling. They provide evidence of a finite-temperature continuous transition with critical exponents $\eta_o=-0.24(4)$ and $\nu_o=2.4(6)$. These results are close to the corresponding estimates that have been obtained in the usual Ising spin-glass model with uncorrelated bond disorder, suggesting that the two models belong to the same universality class. We also determine the leading correction-to-scaling exponent finding $\omega = 1.0(4)$.Comment: 24 pages, 13 figs, J. Stat. Mech. in pres