141 research outputs found
60th birthday of Yurij Holovatch
No full textOn June 16th 2017, Dr. Sci., Professor Yurij Holovatch, Head of the Laboratory for Statistical Physics of Complex Systems, Corresponding Member of the National Academy of Sciences of Ukraine, full member of the Shevchenko Scientific Society, member of the Editorial Board of "Condensed Matter Physics", celebrates his 60th birthday
50th birthday of Yurij Holovatch
No full textIt is easy to write about Yurij Holovatch. As easy as to communicate with him, who is always open, friendly and sincere. It is hard to believe that he is getting 50, we would say, a mature scientific age, as some much younger colleagues could be jealous or dream about his easiness in perceiving novel ideas. On the other hand, his achievements in various fields of theoretical physics make us feel that Prof. Holovatch has been actively working in science considerably longer! More than 70 journal publications, about the same number of conference talks, a supervisor to a dozen of Ph.D. students, editor of six proceedings and scientific books speak for themselves. We are not going to reveal the secret of how he managed all this, but rather leave it for the reader to guess
Predicting the results of the REF using departmental h-index: A look at biology, chemistry, physics, and sociology.
No full textCan metrics be used instead of peer review for REF-type assessments? With the stakes so high, any replacement would have to be extremely accurate. Olesya Mryglod, Ralph Kenna, Yurij Holovatch and Bertrand Berche looked at two metric candidates, including the departmental h-index, and four subject areas: biology, chemistry, physics and sociology. The correlations are significant, but comparisons with RAE indicate that while the departmental h-index is the best metric, it would not have been good enough to replace the peer review exercise. A more important question is whether we should seek to measure research quality using metrics at all
Spreading processes in “post-epidemic” environments. II. Safety patterns on scale-free networks
No full textThis paper continues our previous study on spreading processes in inhomogeneous populations consisting of susceptible and immune individuals (Blavatska and Holovatch, 2021). A special role in such populations is played by “safety patterns” of susceptible nodes surrounded by the immune ones. Here, we analyze spreading on scale-free networks, where the distribution of node connectivity k obeys a power-law decay ∼k-λ. We assume, that only a fraction of p individual nodes can be affected by spreading process, while remaining 1 - p are immune. We apply the synchronous cellular automaton algorithm and study the stationary states and spatial patterning in SI, SIS and SIR models in a range 2 ‹ λ ‹ 3. Two immunization scenarios, the random immunization and an intentional one, that targets the highest degrees nodes are considered. A distribution of safety patterns is obtained for the case of both scenarios. Estimates for the threshold values of the effective spreading rate ßc as a function of active agents fraction and parameter are obtained and efficiency of both vaccination techniques is analyzed quantitatively. The impact of the underlying network heterogeneous structure is manifest e.g. in decreasing the ßc values within the random scenario as compared to corresponding values in the case of regular lattices. This result quantitatively confirms the compliance of scale-free networks for disease spreading. On contrary, the vaccination within the targeted scenario makes the complex networks much more resistant to epidemic spreading as compared with regular lattice structures
The Enigmatic Exponent ⫯ and the Story of Finite-Size Scaling Above the Upper Critical Dimension
No full textScaling, hyperscaling and finite-size scaling were long considered problematic in theories of critical phenomena in high dimensions. The scaling relations themselves form a model-independent structure that any model-specific theory must adhere to, and they are accounted for by the simple principle of homogeneity. Finite-size scaling is similarly founded on the fundamental idea that only two length scales enter the game — namely system length and correlation length. While all scaling relations are quite satisfactory for multitudes of physical systems in low dimensions, one fails in high dimensions. The aberrant scaling relation is called hyperscaling and involves dimensionality itself. Finite-size scaling also appears to fail in high dimensions. Developed in the 1930s, Landau mean-field theory is valid in such high-dimensional systems. However, it too does not accord with hyperscaling and finite-size scaling there. The advent of renormalization-group theory in the 1970s brought deeper fundamental insights into critical phenomena, allowing systems to be viewed at different scales. Above a critical dimensionality, higher-order Renormalization Group (RG) eigenvalues become irrelevant and scaling is governed by the Gaussian fixed point. Although obeying all scaling relations including hyperscaling, and although it appears to successfully explain scaling in the correlation sector, the Gaussian fixed point fails to capture the free energy and derivatives, even in infinite volume. In the 1980s, to fix this for the magnetisation, specific heat and susceptibility, Fisher introduced the notion of dangerous irrelevant variables. Since the correlation sector did not appear to be broken, no attempt was made to repair it and Fisher’s modified RG formalism worked quite well in the thermodynamic limit of infinite volume. However, finite-size scaling fails. Also in the 1980’s, Binder, Nauenberg, Privman and Young extended Fisher’s concept to the free energy itself and to finite-size systems. While putting Fisher’s ideas on a more fundamental footing, the failure of finite-size scaling there still presented a problem. This appeared to be resolved by the introduction of “thermodynamic length” to replace correlation length as the length scale that controls Finite-Size Scaling (FSS). Thus hyperscaling and FSS were both sacrificed in favour of the RG patched together by ad hoc solutions. In the 1990’s, Luijten and Blöte went a long way to resolving the dilemma by adding corrections to scaling to the above considerations. It was clear that both of these played a role. However, as with previous authors, and adhering to the principle of not fixing that appears not to be broken, they did not address correlation length directly.Here we report on developments over the past decade which went a long way to addressing these long-standing problems The key to unlocking these, and extending their validity to the high-dimensional regime, was to relax assumptions that the correlation length has to be bounded by the physical length of bounded systems. This allowed and necessitated the extension of Fisher’s concept of dangerous irrelevant variables to the correlation sector
Scaling and Finite-Size Scaling above the Upper Critical Dimension
No full textIn the 1960's, four famous scaling relations were developed which relate the six standard critical exponents describing continuous phase transitions in the thermodynamic limit of statistical physics models. They are well understood at a fundamental level through the renormalization group. They have been verified in multitudes of theoretical, computational and experimental studies and are firmly established and profoundly important for our understanding of critical phenomena. One of the scaling relations, hyperscaling, fails above the upper critical dimension. There, critical phenomena are governed by Gaussian fixed points in the renormalization-group formalism. Dangerous irrelevant variables are required to deliver the mean-field and Landau values of the critical exponents, which are deemed valid by the Ginzburg criterion. Also above the upper critical dimension, the standard picture is that, unlike for low-dimensional systems, finite-size scaling is non-universal, at least at the critical point. Here we report on new developments which indicate that the current paradigm is flawed and incomplete. In particular, the introduction of a new exponent characterising the finite-size correlation length allows one to extend hyperscaling beyond the upper critical dimension. Moreover, finite-size scaling is shown to be universal provided the correct scaling window is chosen. These recent developments above the upper critical dimension also lead to the introduction of a new scaling relation analogous to one introduced by Fisher 50 years ago and deliver a statistical physics explanation for the emergence of effective four dimensionality as characteristic of generic field theories
Monte Carlo methods for massively parallel computers
No full textApplications that require substantial computational resources today cannot avoid the use of heavily parallel machines. Embracing the opportunities of parallel computing and especially the possibilities provided by a new generation of massively parallel accelerator devices such as GPUs, Intel's Xeon Phi or even FPGAs enables applications and studies that are inaccessible to serial programs. Here we outline the opportunities and challenges of massively parallel computing for Monte Carlo simulations in statistical physics, with a focus on the simulation of systems exhibiting phase transitions and critical phenomena. This covers a range of canonical ensemble Markov chain techniques as well as generalized ensembles such as multicanonical simulations and population annealing. While the examples discussed are for simulations of spin systems, many of the methods are more general and moderate modifications allow them to be applied to other lattice and off-lattice problems including polymers and particle systems. We discuss important algorithmic requirements for such highly parallel simulations, such as the challenges of random-number generation for such cases, and outline a number of general design principles for parallel Monte Carlo codes to perform well
Universal Scaling Relations for Logarithmic-Correction Exponents
No full textBy the early 1960's advances in statistical physics had established the existence of universality classes for systems with second-order phase transitions and characterized these by critical exponents which are different to the classical ones. There followed the discovery of (now famous) scaling relations between the power-law critical exponents describing second-order criticality. These scaling relations are of fundamental importance and now form a cornerstone of statistical mechanics. In certain circumstances, such scaling behaviour is modified by multiplicative logarithmic corrections. These are also characterized by critical exponents, analogous to the standard ones. Recently scaling relations between these logarithmic exponents have been established. Here, the theories associated with these advances are presented and expanded and the status of investigations into logarithmic corrections in a variety of models is reviewed
Geometrical Frustration in Interacting Self-Avoiding Walk Models of Polymers in Dilute Solution
No full textWe look at the effects of geometric frustration in two-dimensional interacting self-avoiding walk models. Models in which these effects are present do not behave in the same way as the standard interacting self-avoiding walk model where an attractive interaction energy is included between non-consecutive, nearest-neighbour visited sites on the lattice. We present, in particular, the different numerical methods we have used to study these models, as well as some of the main results found for a number of different models
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