Statistical Mechanics of Equilibrium and Nonequilibrium Phase Transitions: The Yang-Lee Formalism

Abstract

Showing that the location of the zeros of the partition function can be used to study phase transitions, Yang and Lee initiated an ambitious and very fruitful approach. We give an overview of the results obtained using this approach. After an elementary introduction to the Yang-Lee formalism, we summarize results concerning equilibrium phase transitions. We also describe recent attempts and breakthroughs in extending this theory to nonequilibrium phase transitions.

arXiv comment62 pages, 1 figure, review article submitted to the International Journal of Modern Physics B

References in corpus (64)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Universality classes in nonequilibrium lattice systems
• Phase Transitions in one-dimensional nonequilibrium systems
• General non-existence theorem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions
• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models I. General Theory and Square-Lattice Chromatic Polynomial
• Rules for transition rates in nonequilibrium steady states
• Lee-Yang zeros and phase transitions in nonequilibrium steady states
• The Lee-Yang theory of equilibrium and nonequilibrium phase transitions
• Spatial Particle Condensation for an Exclusion Process on a Ring
• Yang-Lee Theory for a Nonequilibrium Phase Transition
• General Theory of Lee-Yang Zeros in Models with First-Order Phase Transitions
• Partition Function Zeros and Finite Size Scaling of Helix-Coil Transitions in a Polypeptide
• Density of Zeros on the Lee-Yang circle obtained from magnetization data of a two-dimensional Ising ferromagnet
• Asymmetric Exclusion Model and Weighted Lattice Paths
• Exact Finite-Size Scaling and Corrections to Scaling in the Ising Model with Brascamp-Kunz Boundary Conditions
• Detailed balance has a counterpart in non-equilibrium steady states
• Thin Fisher Zeroes
• Complex-Temperature Properties of the 2D Ising Model for Nonzero Magnetic Field
• Yang-Lee zeros of the Q-state Potts model in the complex magnetic-field plane
• Phase Transition Strength through Densities of General Distributions of Zeroes
• Nonequilibrium Dynamics in Low Dimensional Systems
• Finite Size Scaling for O(N) phi^4-Theory at the Upper Critical Dimension
• Some New Results on Complex-Temperature Singularities in Potts Models on the Square Lattice
• The raise and peel model of a fluctuating interface
• Exact Potts Model Partition Function for Strips of the Square Lattice
• Study of the Potts Model on the Honeycomb and Triangular Lattices: Low-Temperature Series and Partition Function Zeros
• Yang-Lee zeros for a nonequilibrium phase transition
• Complex-Temperature Properties of the 2D Ising Model with $\beta H=\pm i\pi /2$
• Partition function zeros at first-order phase transitions: A general analysis
• Nonequilibrium stationary states and equilibrium models with long range interactions
• Identity of the universal repulsive-core singularity with Yang-Lee edge criticality
• Density of the Fisher zeroes for the Ising model
• Partition function zeroes of a self-dual Ising model
• Exact Potts Model Partition Functions for Strips of the Triangular Lattice
• A Generalized Circle Theorem on Zeros of Partition Function at Asymmetric First Order Transitions
• Partition function zeros at first-order phase transitions: Pirogov-Sinai theory
• Matrix Product States of Three Families of One-Dimensional Interacting Particle Systems
• Sharp crossover and anomalously large correlation length in driven systems
• Complex-Temperature Partition Function Zeros of the Potts Model on the Honeycomb and Kagomé Lattices
• Yang-Lee zeroes for an urn model for the separation of sand
• Density of states, Potts zeros, and Fisher zeros of the Q-state Potts model for continuous Q
• Partition function zeros of the Q-state Potts model on the simple-cubic lattice
• Fisher zeros of the Q-state Potts model in the complex temperature plane for nonzero external magnetic field
• Density of Partition Function Zeroes and Phase Transition Strength
• Self-Organized Criticality and Thermodynamic formalism
• Partition Function Zeros for Aperiodic Systems
• Some New Results on Yang-Lee Zeros of the Ising Model Partition Function
• Exact Partition Function for the Potts Model with Next-Nearest Neighbor Couplings on Strips of the Square Lattice
• First Order Phase Transition in a Reaction-Diffusion Model With Open Boundary: The Yang-Lee Theory Approach
• Exact results for the zeros of the partition function of the Potts model on finite lattices
• Yang-Lee Zeros of the Q-state Potts Model on Recursive Lattices
• Exact Shock Profile for the ASEP with Sublattice-Parallel Update
• Partition function zeros of the Q-state Potts model for non-integer Q
• Partition function zeros and leading order scaling correction of the 3D Ising model from multicanonical simulations
• 1D Potts, Yang-Lee Edges and Chaos
• Lee-Yang zeros and the Ising model on the Sierpinski Gasket
• Yang-Lee and Fisher Zeros of Multisite Interaction Ising Models on the Cayley-type Lattices
• Partition Function Zeros of an Ising Spin Glass
• Complex-q zeros of the partition function of the Potts model with long-range interactions
• Anomalous scaling and Lee-Yang zeroes in Self-Organized Criticality
• Lee-Yang Zeroes and Logarithmic Corrections in the ${\Phi }_4^4$ Theory
• Some recent developments in models with absorbing states
• Shock in a Branching-Coalescing Model with Reflecting Boundaries
• Partition function zeros of aperiodic Ising models

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• Density of Yang-Lee zeros for the Ising ferromagnet
• Collapse transition of a square-lattice polymer with next nearest-neighbor interaction
• Probing Yang-Lee Edge Singularity by Central Spin Decoherence
• Universal location of Yang-Lee edge singularity for a one-component field theory in $1\le d\le 4$
• Lee-Yang theory of the Curie-Weiss model and its rare fluctuations
• Yang-Lee Zeros, Semicircle Theorem, and Nonunitary Criticality in Bardeen-Cooper-Schrieffer Superconductivity
• Logarithmic finite-size scaling correction to the leading Fisher zeros in the p-state clock model: A higher-order tensor renormalization group study
• Trajectory phase transitions and dynamical Lee-Yang zeros of the Glauber-Ising chain
• Lee-Yang theory of criticality in interacting quantum many-body systems
• Dynamical Quantum Phase Transition Without An Order Parameter
• Lee-Yang theory of the two-dimensional quantum Ising model
• Zeros of partition functions in the NPT-ensemble
• First-order phase transitions from poles in asymptotic representations of partition functions
• Complex Random Energy Model: Zeros and Fluctuations
• Analytic Partition Function Zeros of the Wako-Saito-Munoz-Eaton beta-hairpin Model
• Disorder lines, modulation, and partition function zeros in free fermion models
• Classical phase transitions in a one-dimensional short-range spin model induced by entropy depletion or complex fields
• Lee-Yang theory of Bose-Einstein condensation
• Low temperature behavior of finite-size one-dimensional Ising model and the partition function zeros
• Detecting the Lee-Yang zeros of a high-spin system by the evolution of probe spin
• Infinite cascades of phase transitions in the classical Ising chain
• The freezing phase transition in hard core lattice gases on triangular lattice with exclusion up to seventh next-nearest neighbor
• Tensor network calculation of the logarithmic correction exponent in the XY model
• Partition-function zeros of spherical spin glasses and their relevance to chaos
• Hard core lattice gas with third next-nearest neighbor exclusion on triangular lattice: one or two phase transitions?
• Exploring Lee-Yang and Fisher Zeros in the 2D Ising model through multipoint Padé approximants
• Signatures of quantum criticality in the complex inverse temperature plane
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• Yang-Lee Zeros of the Yang-Lee Model
• Lee-Yang theory of quantum phase transitions with neural network quantum states
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• Yang-Lee zeros and the critical behavior of the infinite-range two- and three-state Potts models
• Locating Critical Points Using Ratios of Lee-Yang Zeros
• Nonequilibrium phase transition in a single-electron micromaser
• Lee-Yang theory of the superradiant phase transition in the open Dicke model
• Non-Hermitian quantum gases: a platform for imaginary time crystals
• Critical behavior at edge singularities in one dimensional spin models
• Probing the Lee-Yang zeros of a spin bath by correlation functions and entanglement of two spins
• Imaginary-Temperature Zeros for Quantum Phase Transitions
• Stable Yang-Lee zeros in truncated fugacity series from net-baryon number multiplicity distribution
• Motion of Lee-Yang zeros
• Spectral Form Factors of Topological Phases
• Unusual Yang-Lee edge singularity in the one-dimensional axial-next-to-nearest-neighbor Ising model
• Monotonicity of Ursell functions in the Ising model
• From Complexification to Self-Similarity: New Aspects of Quantum Criticality
• A note on Lee-Yang zeros in the negative half-plane
• Lee-Yang-zero ratio method in three-dimensional Ising model
• Extracting partition function zeros from Fukui-Todo simulations
• Low-temperature series expansion of square lattice Ising model: A study based on Fisher zeros
• Partition function zeros of zeta-urns
• When correlations exceed system size: finite-size scaling in free boundary conditions above the upper critical dimension
• Yang-Lee Zeros of Certain Antiferromagnetic Models
• Lee-Yang formalism for phase transitions of interacting fermions using tensor networks
• The location of the Fisher zeros and estimates of yT = 1/ν are found for the Baxter-Wu model
• Partition function zeros of quantum many-body systems
• Condensation of Lee-Yang zeros in scalar field theory
• Modified Yang-Lee theory for nonlocal gravitational potential and their phase transition
• Phase diagram of the Wako-Saito-Munoz-Eaton beta-hairpin Model obtained with partition function zeros
• Yang-Lee Zeros of 2D Nearest-Neighbor Antiferromagnetic Ising Models: A Numerical Linked Cluster Expansion Study
• Discontinuous Phase Transition in an Exactly Solvable One-Dimensional Creation-Annihilation System
• A Microcanonical Inflection Point Analysis via Parametric Curves and its Relation to the Zeros of the Partition Function
• Yang-Lee zeros for real-space condensation
• Partition Function Zeros of Paths and Normalization Zeros of ASEPS
• Detecting the purely imaginary Fisher zeros of an Ising spin system on a quantum computer
• Dynamical quantum phase transitions in strongly correlated two-dimensional spin lattices following a quench
• A numerical study of the zeros of the grand partition function of $k$-mers on strips of width $k$
• A geometric conjecture about phase transitions
• A standard CLT for triangles in a class of ERGs
• A Dynamical Bulk-Boundary Correspondence in Two Dimensional Topological Matter
• Fermi surface as a quantum critical manifold: gaplessness, order parameter, and scaling in $d$-dimensions
• Yang-Lee and Fisher zeros generalized on some far-from-equilibrium systems
• Asymptotic methods for confined fluids
• Hierarchy of percolation patterns in a kinetic replication model