Related papers: Phase transition modelling of relapse in major dep…
In the context of the dynamical mean-field theory of the Hubbard model, we identify microscopically an order parameter for the finite temperature Mott endpoint. We derive a Landau functional of the order parameter. We then use the order…
We introduce a toy model, which represents a simplified version of the problem of the depinning transition in the limit of strong disorder. This toy model can be formulated as a simple renormalization transformation for the probability…
In this review article, we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked…
Change-point detection methods are proposed for the case of temporary failures, or transient changes, when an unexpected disorder is ultimately followed by a readjustment and return to the initial state. A base distribution of the…
Mixed order transitions are those which show a discontinuity of the order parameter as well as a divergent correlation length. We show that the behaviour of the order parameter correlation function along the transition line of mixed order…
Model studies indicate that many climate subsystems, especially ecosystems, may be vulnerable to 'tipping': a 'catastrophic process' in which a system, driven by gradually changing external factors, abruptly transitions (or 'collapses')…
Continuous phase transitions associated with the onset of a spontaneously broken symmetry are thought to be successfully described by the Landau-Ginzburg-Wilson-Fisher theory of fluctuating order parameters. In this work we show that such…
Symmetry provides important insight in understanding the nature of phase transitions. In the presence of crystalline symmetries, new phenomena in phase transition can emerge, such as intertwined orders and emergent symmetries. In this work,…
The effects of an aperiodic order or a random disorder on phase transitions in statistical mechanics are discussed. A heuristic relevance criterion based on scaling arguments as well as specific results for Ising models with random disorder…
External and internal factors may cause a system's parameter to vary with time before it stabilizes. This drift induces a regime shift when the parameter crosses a bifurcation. Here, we study the case of an infinite dimensional system: a…
We discuss the nonlinear phenomena of irreversible tipping for non-autonomous systems where time-varying inputs correspond to a smooth "parameter shift" from one asymptotic value to another. We express tipping in terms of pullback…
The identification and classification of transitions in topological and microstructural regimes in pattern-forming processes are critical for understanding and fabricating microstructurally precise novel materials in many application…
We study the influence of a correlated disorder on the localization phase transition in the pinning model. When correlations are strong enough, a strong disorder regime arises: large and frequent attractive regions appear in the…
The Landau paradigm of phase transitions is one of the backbones in critical phenomena. With a $Z_2$ symmetry, it describes the Ising universality class whose central charge is one half (c = 1=2) in two spatial dimensions (2D). Recent…
Nonlinear dynamical systems subjected to a combination of noise and time-varying forcing can exhibit sudden changes, critical transitions or tipping points where large or rapid dynamic effects arise from changes in a parameter that are…
The nature of phase transitions involving the questions why and how phase transitions take place has not been sufficiently touched in the literature. In contrast, the current attention to certain extent still focus on the description of…
In clean and weakly disordered systems, topological and trivial phases having a finite bulk energy gap can transit to each other via a quantum critical point. In presence of strong disorder, both the nature of the phases and the associated…
We consider the formalism of information decomposition of target effects from multi-source interactions, i.e. the problem of defining redundant and synergistic components of the information that a set of source variables provides about a…
The rupture of a medium under stress typifies breakdown phenomena. More generally, the latter encompass the dynamics of systems of many interacting elements governed by the interplay of a driving force with a pinning disorder, resulting in…
We apply modern methods in computational topology to the task of discovering and characterizing phase transitions. As illustrations, we apply our method to four two-dimensional lattice spin models: the Ising, square ice, XY, and…