Fields, particles and universality in two dimensions

Abstract

We discuss the use of field theory for the exact determination of universal properties in two-dimensional statistical mechanics. After a compact derivation of critical exponents of main universality classes, we turn to the off-critical case, considering systems both on the whole plane and in presence of boundaries. The topics we discuss include magnetism, percolation, phase separation, interfaces, wetting.

58 pages, 19 figures. Expanded notes of lectures given at the school "Statistical Field Theories", GGI Arcetri, Florence, February 2015; v2: references added

References in corpus (53)

• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• Logarithmic Operators in Conformal Field Theory
• Critical Percolation in Finite Geometries
• SLE for theoretical physicists
• Non-integrable Quantum Field Theories as Perturbations of Certain Integrable Models
• 2D growth processes: SLE and Loewner chains
• Boundary energy and boundary states in integrable quantum field theories
• Filling transition for a wedge
• Geometry dominated fluid adsorption on sculptured substrates
• Non-integrable aspects of the multi-frequency Sine-Gordon model
• Asymptotic factorisation of form factors in two-dimensional quantum field theory
• The Spin-Spin Correlation Function in the Two-Dimensional Ising Model in a Magnetic Field at $T=T_c$
• Form-factors of exponential fields in the sine-Gordon model
• Factorized Scattering in the Presence of Reflecting Boundaries
• Linking numbers for self-avoiding walks and percolation: application to the spin quantum Hall transition
• Integrable field theory and critical phenomena. The Ising model in a magnetic field
• Universal amplitude ratios in the two-dimensional $q$-state Potts model and percolation from quantum field theory
• Logarithmic Conformal Field Theory: a Lattice Approach
• SLE_k growth processes and conformal field theories
• Decay of particles above threshold in the Ising field theory with magnetic field
• Massless Flows II: the exact S-matrix approach
• Universal ratios along a line of critical points. The Ashkin--Teller model
• Universal amplitude ratios in the two-dimensional Ising model
• Covariance for Conic and Wedge Complete Filling
• Non compact conformal field theory and the a_2^{(2)} (Izergin-Korepin) model in regime III
• Confinement in the q-state Potts field theory
• Phase separation in a wedge. Exact results
• One-point functions in perturbed boundary conformal field theories
• Off-critical correlations in the Ashkin-Teller model
• Critical exponents of domain walls in the two-dimensional Potts model
• Phase separation and interface structure in two dimensions from field theory
• Parafermionic excitations and critical exponents of random cluster and O(n) models
• Particle spectrum of the 3-state Potts field theory: a numerical study
• Exact theory of intermediate phases in two dimensions
• Ward Identities and Integrable Differential Equations in the Ising Field Theory
• Boundary one-point function, Casimir energy and boundary state formalism in D+1 dimensional QFT
• Field theory of Ising percolating clusters
• Unusual corrections to scaling in the 3-state Potts antiferromagnet on a square lattice
• Critical amplitude ratios of the Baxter-Wu model
• The Field Theory of the q->4+ Potts Model
• Interfaces and wetting transition on the half plane. Exact results from field theory
• First order phase transitions and integrable field theory. The dilute q-state Potts model
• Universal amplitude ratios of two-dimensional percolation from field theory
• Integrable aspects of the scaling q-state Potts models II: finite-size effects
• Ising Spectroscopy II: Particles and poles at T>Tc
• Two-kink bound states in the magnetically perturbed Potts field theory at T<Tc
• On the space of quantum fields in massive two-dimensional theories
• High-precision determination of universal amplitude ratios for the q=3 Potts model in 2d
• Bulk and boundary effects on the decay of the thermodynamic Casimir force
• The Universal Amplitude Ratio ${\Gamma }^{-}/{\Gamma }^{+}$ for Two-Dimensional Percolation
• Boundary S-matrix for the Integrable q-Potts Model
• Crossing probability and number of crossing clusters in off-critical percolation
• Correlation functions of disorder operators in massive ghost theories

Cited by in corpus (18)

• Entanglement of the $3$-State Potts Model via Form Factor Bootstrap: Total and Symmetry Resolved Entropies
• Lectures on S-matrices and Integrability
• Classifying Potts critical lines
• Exact results for quenched bond randomness at criticality
• On superuniversality in the $q$-state Potts model with quenched disorder
• Multiple phases and vicious walkers in a wedge
• Long range correlations generated by phase separation. Exact results from field theory
• Critical points of coupled vector-Ising systems. Exact results
• Critical percolation in the slow cooling of the bi-dimensional ferromagnetic Ising model
• Absence of nematic quasi-long-range order in two-dimensional liquid crystals with three director components
• Exact results for the $O(N)$ model with quenched disorder
• Critical lines in the pure and disordered $O(N)$ model
• On the phase diagram of the random bond $q$-state Potts model
• Interface localization near criticality
• Critical points in the $R{P}^{N-1}$ model
• Critical points in the $C{P}^{N-1}$ model
• Exact results for spin glass criticality
• The critical Barkhausen avalanches in thin random-field ferromagnets with an open boundary