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"Phase transformations (Statistical physics)"
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Universality in nonequilibrium lattice systems
Universal scaling behavior is an attractive feature in statistical physics because a wide range of models can be classified purely in terms of their collective behavior due to a diverging correlation length. This book provides a comprehensive overview of dynamical universality classes occurring in nonequilibrium systems defined on regular lattices. The factors determining these diverse universality classes have yet to be fully understood, but the book attempts to summarize our present knowledge, taking them into account systematically.
eBook
The Mother Body Phase Transition in the Normal Matrix Model
The normal matrix model with algebraic potential has gained a lot of attention recently, partially in virtue of its connection to
several other topics as quadrature domains, inverse potential problems and the Laplacian growth.
In this present paper we
consider the normal matrix model with cubic plus linear potential. In order to regularize the model, we follow Elbau & Felder and
introduce a cut-off. In the large size limit, the eigenvalues of the model accumulate uniformly within a certain domain
We also study in detail the mother body problem associated to
To construct the mother body measure, we define a quadratic differential
Following previous works of Bleher & Kuijlaars
and Kuijlaars & López, we consider multiple orthogonal polynomials associated with the normal matrix model. Applying the Deift-Zhou
nonlinear steepest descent method to the associated Riemann-Hilbert problem, we obtain strong asymptotic formulas for these polynomials.
Due to the presence of the linear term in the potential, there are no rotational symmetries in the model. This makes the construction of
the associated
eBook
Phase Transitions and Renormalization Group
This book provides an elementary introduction to the notions of continuum limit and universality in statistical systems with a large number of degrees of freedom. The existence of a continuum limit requires the appearance of correlations at large distance, a situation that is encountered in second order phase transitions, near the critical temperature. In this context, the book emphasizes the role of gaussian distributions and their relations with the mean field approximation and Landau′s theory of critical phenomena. The book shows that quasi-gaussian or mean-field approximations cannot describe correctly phase transitions in three space dimensions. The book assigns this difficulty to the coupling of very different physical length scales, even though the systems we will consider have only local, that is, short range, interactions. To analyze the unusual situation, a new concept is required: the renormalization group, whose fixed points allow understanding the universality of physical properties at large distance, beyond mean-field theory. In the continuum limit, critical phenomena can be described by quantum field theories. In this framework, the renormalization group is directly related to the renormalization process; that is, the necessity to cancel the infinities that arise in straightforward formulations of the theory. The book discusses the renormalization group in the context of various relevant field theories. This leads to proofs of universality and to efficient tools for calculating universal quantities in a perturbative framework. Finally, the book constructs a general functional renormalization group, which can be used when perturbative methods are inadequate.
eBook
Quantum Phase Transitions
Describing the physical properties of quantum materials near critical points with long-range many-body quantum entanglement, this book introduces readers to the basic theory of quantum phases, their phase transitions and their observable properties. This second edition begins with a new section suitable for an introductory course on quantum phase transitions, assuming no prior knowledge of quantum field theory. It also contains several new chapters to cover important recent advances, such as the Fermi gas near unitarity, Dirac fermions, Fermi liquids and their phase transitions, quantum magnetism, and solvable models obtained from string theory. After introducing the basic theory, it moves on to a detailed description of the canonical quantum-critical phase diagram at non-zero temperatures. Finally, a variety of more complex models are explored. This book is ideal for graduate students and researchers in condensed matter physics and particle and string theory.
eBook
Phase Transitions in Solids Under High Pressure
High-pressure research has become increasingly important, and high-pressure techniques are an invaluable tool for synthesizing new materials and discovering novel physical phenomena that are not accessible at ambient pressure. This text deals with the problem of phase transitions in solids at high pressure. It covers phase equilibria at high pressures in various materials, the deformation impact on phase transformations at high pressures, high-temperature and low-temperature transformation kinetics and hysteresis at high pressures, and the requirements for obtaining and maintaining high-pressure phases.
eBook
Stochastic Spatial Models in Ecology: A Statistical Physics Approach
Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales. Ecological neutral theory has provided simple predictions accounting for general empirical patterns in communities of competing species. However, while neutral theory in well-mixed ecosystems is mathematically well understood, spatial models still present several open problems, limiting the quantitative understanding of spatial biodiversity. In this review, we discuss the state of the art in spatial neutral theory. We emphasize the connection between spatial ecological models and the physics of non-equilibrium phase transitions and how concepts developed in statistical physics translate in population dynamics, and vice versa. We focus on non-trivial scaling laws arising at the critical dimension D=2 of spatial neutral models, and their relevance for biological populations inhabiting two-dimensional environments. We conclude by discussing models incorporating non-neutral effects in the form of spatial and temporal disorder, and analyze how their predictions deviate from those of purely neutral theories.
Journal Article
Extreme States of Matter in Strong Interaction Physics
The thermodynamics of strongly interacting matter remains a profound and challenging area of modern physics, both in theory and experiment. This book offers newcomers an introduction to the field that emphasizes basic concepts and ideas.
eBook
Scaling Invariance: A Gateway to Phase Transitions
We explore the concept of scaling invariance in a type of dynamical systems that undergo a transition from regularity to chaos. The systems are described by a two-dimensional, nonlinear mapping that preserves the area in the phase space. The key variables are the action and the angle, as usual from Hamiltonian systems. The transition is influenced by a control parameter giving the form of the order parameter. We observe a scaling invariance in the average squared action within the chaotic region, providing evidence that this change from regularity (integrability) to chaos (non-integrability) is akin to a second-order or continuous phase transition. As the order parameter approaches zero, its response against the variation in the control parameter (susceptibility) becomes increasingly pronounced (indeed diverging), resembling a phase transition.
Journal Article
Quantum statistical mechanics in classical phase space
Quantum Statistical Mechanics in Classical Phase Space offers not just a new computational approach to condensed matter systems, but also a unique conceptual framework for understanding the quantum world and collective molecular behaviour. A formally exact transformation, this revolutionary approach goes beyond the quantum perturbation of classical condensed matter to applications that lie deep in the quantum regime.
eBook