Inhomogeneous Systems with Unusual Critical Behaviour

Abstract

The phase transitions and critical properties of two types of inhomogeneous systems are reviewed. In one case, the local critical behaviour results from the particular shape of the system. Here scale-invariant forms like wedges or cones are considered as well as general parabolic shapes. In the other case the system contains defects, either narrow ones in the form of lines or stars, or extended ones where the couplings deviate from their bulk values according to power laws. In each case the perturbation may be irrelevant, marginal or relevant. In the marginal case one finds local exponents which depend on a parameter. In the relevant case unusual stretched exponential behaviour and/or local first order transitions appear. The discussion combines mean field theory, scaling considerations, conformal transformations and perturbation theory. A number of examples are Ising models for which exact results can be obtained. Some walks and polymer problems are considered, too.

78 pages, Plain TeX and epsf, 16 postscript-figures

References in corpus (8)

• Conformal invariance and linear defects in the two-dimensional Ising model
• Anisotropic critical phenomena in parabolic geometries: the directed self-avoiding walk
• The quantum Ising chain with a generalized defect
• Critical behaviour in parabolic geometries
• Radial marginal perturbation of two-dimensional systems and conformal invariance
• Surface Magnetization of Aperiodic Ising Quantum Chains
• Marginal Extended Perturbations in Two Dimensions and Gap-Exponent Relations
• Nonanalytic correlation length in Ising systems with one surface defect line

Cited by in corpus (90)

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• The Random Transverse Ising Spin Chain and Random Walks
• Capture of the Lamb: Diffusing Predators Seeking a Diffusing Prey
• Critical phenomena at perfect and non-perfect surfaces
• Reaction-Diffusion Processes from Equivalent Integrable Quantum Chains
• Statistical Models with a Line of Defect
• Kinetics of a Diffusive Capture Process: Lamb Besieged by a Pride of Lions
• Solution of the fermionic entanglement problem with interface defects
• Entanglement entropy with localized and extended interface defects
• Water in nanopores. II. Liquid-vapour phase transition near hydrophobic surfaces
• Entanglement entropy of aperiodic quantum spin chains
• Emergent spatial structures in critical sandpiles
• Critical Binder cumulant of two-dimensional Ising models
• Quantum spins on star graphs and the Kondo model
• Quantum transitions driven by one-bond defects in quantum Ising rings
• Quantum Ising chains with boundary fields
• Entanglement in one-dimensional critical state after measurements
• Density Profiles in Random Quantum Spin Chains
• Nonlocality and entanglement in measured critical quantum Ising chains
• Magnetic critical behavior of two-dimensional random-bond Potts ferromagnets in confined geometries
• Aging phenomena in critical semi-infinite systems
• Entanglement asymmetry in CFT and its relation to non-topological defects
• Does hardcore interaction change absorbing type critical phenomena?
• Critical adsorption near edges
• Gradient critical phenomena in the Ising quantum chain
• Non-equilibrium quantum dynamics after local quenches
• Entanglement entropy and negativity in the Ising model with defects
• Bulk and surface properties in the critical phase of the two-dimensional XY model
• Out-of-equilibrium critical dynamics at surfaces: Cluster dissolution and non-algebraic correlations
• Finite-size effects in layered magnetic systems
• Relevant Aperiodic Modulation in the 2d Ising Model
• Exact solution of the $2d$ dimer model: Corner free energy, correlation functions and combinatorics
• Fractal Dimensions of Confined Clusters in Two-Dimensional Directed Percolation
• Gradient critical phenomena in the Ising quantum chain: surface behaviour
• Mixed-order phase transition of the contact process near multiple junctions
• Critical adsorption and Casimir torque in wedges and at ridges
• Nonequilibrium critical dynamics in inhomogeneous systems
• Non-equilibrium Dynamics Following a Quench to the Critical Point in a Semi-infinite System
• Surface Shape and Local Critical Behaviour in Two-Dimensional Directed Percolation
• Nonequilibrium phase transition in a driven Potts model with friction
• Logarithmic delocalization of end spins in the S=3/2 antiferromagnetic Heisenberg chain
• Corner Exponents in the Two-Dimensional Potts Model
• Surface-induced disorder and aperiodic perturbations at first-order transitions
• Strong disorder renormalization group study of aperiodic quantum Ising chains
• Ising cubes with enhanced surface couplings
• Universal scaling of a classical impurity in the quantum Ising chain
• Evolution of the magnetization after a local quench in the critical transverse-field Ising chain
• Percolation and Conduction in Restricted Geometries
• A unified treatment of Ising model magnetizations
• Conformal Profiles in the Hilhorst--van Leeuwen Model
• One-dimensional Bose gas driven by a slow time-dependent harmonic trap
• Edge critical behavior at the surface transition of Ising magnets
• Local critical behaviour at aperiodic surface extended perturbation in the Ising quantum chain
• Transverse-field Ising spin chain with inhomogeneous disorder
• Logarithmic corrections in the two-dimensional Ising model in a random surface field
• Observation of mixed anisotropy in the critical susceptibility of an ultrathin magnetic film
• Local aging phenomena close to magnetic surfaces
• Critical behavior of nanocrystalline gadolinium: Evidence for a new universality class
• The critical Ising model on a torus with a defect line
• Extended surface disorder in the quantum Ising chain
• Three-dimensional non-equilibrium Potts systems with magnetic friction
• Entanglement entropy of the $Q\ge 4$ quantum Potts chain
• Ising thin films with modulations and surface defects
• Critical behavior of the spin correlation function in Ashkin-Teller and Baxter models with a line defect
• Spin correlation function in 2D statistical mechanics models with inhomogeneous line defects
• Impurity-driven transitions in frustrated quantum Ising ring
• Nonequilibrium critical relaxation at a first-order phase transition point
• Reentrance during nonequilibrium relaxation
• Realization of supersymmetric quantum mechanics in inhomogeneous Ising models
• Phase transitions at surfaces, edges, and corners
• Scaling properties at the interface between different critical subsystems: The Ashkin-Teller model
• Critical behavior at the interface between two systems belonging to different universality classes
• On the finite-size effects in two segregated Bose-Einstein condensates restricted by a hard wall
• Entanglement across extended random defects in the XX spin chain
• Gradual Diffusive Capture: Slow Death by Many Mosquito Bites
• Nonuniversal and anomalous critical behavior of the contact process near an extended defect
• Exact solution of the critical Ising model with special toroidal boundary conditions
• Numerical study of the critical behavior of the Ashkin-Teller model at a line defect
• Boundary critical phenomena of the random transverse Ising model in D>=2 dimensions
• Radial Fredholm perturbation in the two-dimensional Ising model and gap-exponent relation
• Deep Boundary Perturbations at a Quantum Critical Point
• The quantum XY chain with boundary fields: finite-size gap and phase behavior
• Massive ghost theories with a line of defects
• Multiscaling in Ising quantum chains with random Hilhorst-van Leeuwen perturbations
• Iterated star-triangle transformation on inhomogeneous 2D Ising lattices
• Anomalous diffusion in a space- and time-dependent energy landscape
• Reduction of surface coverage of finite systems due to geometrical steps