Statistical mechanics of glass transition in lattice molecule models

Lattice molecule models are proposed in order to study statistical mechanics of glass transition in finite dimensions. Molecules in the models are represented by hard Wang tiles and their density is controlled by a chemical potential. An infinite series of irregular ground states are constructed theoretically. By defining a glass order parameter as a collection of the overlap with each ground state, a thermodynamic transition to a glass phase is found in a stratified Wang tiles model on a cubic lattice.Comment: 18 pages, 8 figure

Approaches, Strategies and Theoretical and Practice-Based Research Methods to investigate and archive video art:Some reflections from the REWIND projects

This paper will discuss methodologies, approaches and issues, emerging out of three major research projects that have investigated early histories of video art in Europe: REWIND (2004 ongoing), REWINDItalia (2011-2014) and EWVA (2015-2018). The paper will discuss how the projects have engaged with the history of the apparatus, the identity and status of the artworks, preservation methods, and the legacy of these video artworks today. A particular focus will be on semi-structured questionnaires for interviews structured to capture oral histories, memories and recollections, that in some cases would have been otherwise lost to future knowledge and the uncovering of lost artworks and their available documentation. The speakers directly involved in the projects - will discuss solutions, risks and experiences encountered in the projects and future research perspectives for re-covering, collecting, archiving and narrating the histories of early video art in Europe. The paper will discuss also different practice-based research methods, platforms and engagement strategies, including re-installation and re-enactment

Modelling quasicrystals at positive temperature

We consider a two-dimensional lattice model of equilibrium statistical mechanics, using nearest neighbor interactions based on the matching conditions for an aperiodic set of 16 Wang tiles. This model has uncountably many ground state configurations, all of which are nonperiodic. The question addressed in this paper is whether nonperiodicity persists at low but positive temperature. We present arguments, mostly numerical, that this is indeed the case. In particular, we define an appropriate order parameter, prove that it is identically zero at high temperatures, and show by Monte Carlo simulation that it is nonzero at low temperatures

A test of non-equilibrium thermodynamics in glassy systems: the soft-sphere case

The scaling properties of the soft-sphere potential allow the derivation of an exact expression for the pressure of a frozen liquid, i.e., the pressure corresponding to configurations which are local minima in its multidimensional potential energy landscape. The existence of such a relation offers the unique possibility for testing the recently proposed extension of the liquid free energy to glassy out-of-equilibrium conditions and the associated expression for the temperature of the configurational degrees of freedom. We demonstrate that the non-equilibrium free energy provides an exact description of the soft-sphere pressure in glass states

Reconstructing nonparametric productivity networks

Network models provide a general representation of inter-connected system dynamics. This ability to connect systems has led to a proliferation of network models for economic productivity analysis, primarily estimated non-parametrically using Data Envelopment Analysis (DEA). While network DEA models can be used to measure system performance, they lack a statistical framework for inference, due in part to the complex structure of network processes. We fill this gap by developing a general framework to infer the network structure in a Bayesian sense, in order to better understand the underlying relationships driving system performance. Our approach draws on recent advances in information science, machine learning and statistical inference from the physics of complex systems to estimate unobserved network linkages. To illustrate, we apply our framework to analyze the production of knowledge, via own and cross-disciplinary research, for a world-country panel of bibliometric data. We find significant interactions between related disciplinary research output, both in terms of quantity and quality. In the context of research productivity, our results on cross-disciplinary linkages could be used to better target research funding across disciplines and institutions. More generally, our framework for inferring the underlying network production technology could be applied to both public and private settings which entail spillovers, including intra-and inter-firm managerial decisions and public agency coordination. This framework also provides a systematic approach to model selection when the underlying network structure is unknown

Inherent Structures in models for fragile and strong glass

An analysis of the dynamics is performed, of exactly solvable models for fragile and strong glasses, exploiting the partitioning of the free energy landscape in inherent structures. The results are compared with the exact solution of the dynamics, by employing the formulation of an effective temperature used in literature. Also a new formulation is introduced, based upon general statistical considerations, that performs better. Though the considered models are conceptually simple there is no limit in which the inherent structure approach is exact.Comment: 19 pages, 4 figure

Order in glassy systems

A directly measurable correlation length may be defined for systems having a two-step relaxation, based on the geometric properties of density profile that remains after averaging out the fast motion. We argue that the length diverges if and when the slow timescale diverges, whatever the microscopic mechanism at the origin of the slowing down. Measuring the length amounts to determining explicitly the complexity from the observed particle configurations. One may compute in the same way the Renyi complexities K_q, their relative behavior for different q characterizes the mechanism underlying the transition. In particular, the 'Random First Order' scenario predicts that in the glass phase K_q=0 for q>x, and K_q>0 for q<x, with x the Parisi parameter. The hypothesis of a nonequilibrium effective temperature may also be directly tested directly from configurations.Comment: Typos corrected, clarifications adde

Spin-Glass Model for Inverse Freezing

We analyze the Blume-Emery-Griffiths model with disordered magnetic interaction displaying the inverse freezing phenomenon. The behaviour of this spin-1 model in crystal field is studied throughout the phase diagram and the transition and spinodal lines for the model are computed using the Full Replica Symmetry Breaking Ansatz that always yelds a thermodynamically stable phase. We compare the results both with the quenched disordered model with Ising spins on lattice gas - where no reentrance takes place - and with the model with generalized spin variables recently introduced by Schupper and Shnerb [Phys. Rev. Lett. 93, 037202 (2004)]. The simplest version of all these models, known as Ghatak-Sherrington model, turns out to hold all the general features characterizing an inverse transition to an amorphous phase, including the right thermodynamic behavior.Comment: 6 pages, 4 figures, to appear in the Proceeding for the X International Workshop on Disordered Systems (2006), Molveno, Ital

The random K-satisfiability problem: from an analytic solution to an efficient algorithm

We study the problem of satisfiability of randomly chosen clauses, each with K Boolean variables. Using the cavity method at zero temperature, we find the phase diagram for the K=3 case. We show the existence of an intermediate phase in the satisfiable region, where the proliferation of metastable states is at the origin of the slowdown of search algorithms. The fundamental order parameter introduced in the cavity method, which consists of surveys of local magnetic fields in the various possible states of the system, can be computed for one given sample. These surveys can be used to invent new types of algorithms for solving hard combinatorial optimizations problems. One such algorithm is shown here for the 3-sat problem, with very good performances.Comment: 38 pages, 13 figures; corrected typo

Thermodynamic glass transition in a spin glass without time-reversal symmetry

Spin glasses are a longstanding model for the sluggish dynamics that appears at the glass transition. However, spin glasses differ from structural glasses for a crucial feature: they enjoy a time reversal symmetry. This symmetry can be broken by applying an external magnetic field, but embarrassingly little is known about the critical behaviour of a spin glass in a field. In this context, the space dimension is crucial. Simulations are easier to interpret in a large number of dimensions, but one must work below the upper critical dimension (i.e., in d<6) in order for results to have relevance for experiments. Here we show conclusive evidence for the presence of a phase transition in a four-dimensional spin glass in a field. Two ingredients were crucial for this achievement: massive numerical simulations were carried out on the Janus special-purpose computer, and a new and powerful finite-size scaling method.Comment: 10 pages, 6 figure