A scaling theory for the long-range to short-range crossover and an infrared duality

Abstract

We study the second-order phase transition in the $d$-dimensional Ising model with long-range interactions decreasing as a power of the distance $1/r^{d+s}$. For $s$ below some known value $s_{\ast }$, the transition is described by a conformal field theory without a local stress tensor operator, with critical exponents varying continuously as functions of $s$. At $s=s_{\ast }$, the phase transition crosses over to the short-range universality class. While the location $s_{\ast }$ of this crossover has been known for 40 years, its physics has not been fully understood, the main difficulty being that the standard description of the long-range critical point is strongly coupled at the crossover. In this paper we propose another field-theoretic description which, on the contrary, is weakly coupled near the crossover. We use this description to clarify the nature of the crossover and make predictions about the critical exponents. That the same long-range critical point can be reached from two different UV descriptions provides a new example of infrared duality.

57pp, detailed version of arXiv:1703.03430, v2: misprints corrected, v3: refs and discussion of log corrections at the crossover added, v4: published version plus extra comments in appendix A,B and an acknowledgement, v5: published version plus extra comments in appendix A,B and an acknowledgement (replacing the wrong tex file of v4)

References in corpus (13)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Central Charge Bounds in 4D Conformal Field Theory
• Long-range critical exponents near the short-range crossover
• The crossover region between long-range and short-range interactions for the critical exponents
• Conformal perturbation theory beyond the leading order
• A Complete Renormalization Group Trajectory Between Two Fixed Points
• Conformal Field Theory and Statistical Mechanics
• O(N) and O(N) and O(N)
• Leading Order Anomalous Dimensions at the Wilson-Fisher Fixed Point from CFT
• Non-gaussianity of the critical 3d Ising model
• Critical behavior of the Ising model with long range interactions

Cited by in corpus (86)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
• Criticality and Phase Diagram of Quantum Long-Range $\text{O(N)}$ models
• The Analytic Functional Bootstrap I: 1D CFTs and 2D S-Matrices
• The Analytic Functional Bootstrap II: Natural Bases for the Crossing Equation
• A Study of Quantum Field Theories in AdS at Finite Coupling
• A tauberian theorem for the conformal bootstrap
• The 3d Stress-Tensor Bootstrap
• Line and surface defects for the free scalar field
• Bootstrapping the long-range Ising model in three dimensions
• The Gross-Neveu-Yukawa Archipelago
• Criticality of Spin Systems with Weak Long-Range Interactions
• 3d Abelian Gauge Theories at the Boundary
• Bootstrapping boundary-localized interactions
• Bootstrapping the 3d Ising Stress Tensor
• Anomalous Dimensions in the WF O($N$) Model with a Monodromy Line Defect
• $O(N)$ Models with Boundary Interactions and their Long Range Generalizations
• On Higher-Spin Points and Infinite Distances in Conformal Manifolds
• Geodesic bulk diagrams on the Bruhat-Tits tree
• Bootstrapping boundary-localized interactions II: Minimal models at the boundary
• Quantum criticality and excitations of a long-range anisotropic $XY$-chain in a transverse field
• Scaling the semidefinite program solver SDPB
• Coupled minimal models revisited
• Critical two-point function for long-range $O(n)$ models below the upper critical dimension
• Long-range multi-scalar models at three loops
• Complex networks with tuneable dimensions as a universality playground
• Gauge Theories with Ultracold Atoms
• Gentle introduction to rigorous Renormalization Group: a worked fermionic example
• The unitary subsector of generalized minimal models
• Introduction to Lightcone Conformal Truncation: QFT Dynamics from CFT Data
• Finite-temperature critical behaviors in 2D long-range quantum Heisenberg model
• Operator mixing in $\mathbf{\epsilon }$-expansion: scheme and evanescent (in)dependence
• Non-local non-linear sigma models
• Renormalization and conformal invariance of non-local quantum electrodynamics
• Hyperbolic Lattice for Scalar Field Theory in AdS${}_3$
• Conformal perturbation theory
• Topological edge modes and phase transition in the critical fermionic chain with long-range interaction
• Lining up a Positive Semi-Definite Six-Point Bootstrap
• A model of persistent breaking of continuous symmetry
• The F-theorem in the melonic limit
• Ising chains with competing interactions in presence of long-range couplings
• Analytic and numerical bootstrap for the long-range Ising model
• Bounding 3d CFT correlators
• Sharp hierarchical upper bounds on the critical two-point function for long-range percolation on ${\mathbb{Z}}^d$
• Long Range, Large Charge, Large $N$
• Remarks on a melonic field theory with cubic interaction
• Self-consistent harmonic approximation with non-local couplings
• Instability of complex CFTs with operators in the principal series
• A CFT Distance Conjecture
• Finite-size versus finite-temperature effects in the critical long-range $O(N)$ model
• Polyakov's confinement mechanism for generalized Maxwell theory
• Quantum criticality of a ${\mathbb{Z}}_3$ symmetric spin chain with long-range interactions
• Long-range fermions and critical dualities
• Coupled minimal models revisited II: Constraints from permutation symmetry
• Universality in long-range interacting systems: the effective dimension approach
• Anomalous dimensions of partially-conserved higher-spin currents from conformal field theory: bosonic ${\varphi }^{2n}$ theories
• 1d Ising model with $1/r^{1.99}$ interaction
• Mixed field theory
• Effective-Dimension Theory of Critical Phenomena above Upper Critical Dimensions
• Sextic tensor model in rank $3$ at next-to-leading order
• Universal scaling in real dimension
• Critical phase induced by Berry phase and dissipation in a spin chain
• Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges
• Sphere free energy of scalar field theories with cubic interactions
• Sextic tensor field theories in rank $3$ and $5$
• Tensor Field Theories: Renormalization and Random Geometry
• 3d Large $N$ Vector Models at the Boundary
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories
• Two-dimensional Ising and Potts model with long-range bond disorder: a renormalization group approach
• One-loop functional renormalization group study for the dimensional reduction and its breakdown in the long-range random field O($N$) spin model near lower critical dimension
• Stochastic parameter optimization analysis of dynamical quantum critical phenomena in long-range transverse-field Ising chain
• Long-Range Vector Models at Large N
• Critical long-range vector model in the UV
• Dynamic critical exponent in quantum long-range models
• Energy trapped Ising model
• RG studies of scalar-field models of long-range interactions
• Critical and multicritical Lee-Yang fixed points in the local potential approximation
• Long-range spin glass in a field at zero temperature
• Bootstrap Method in Theoretical Physics
• Exact four-point function and OPE for an interacting quantum field theory with space/time anisotropic scale invariance
• Light cone OPE in a CFT with lowest twist scalar primary
• Boundary anomalous dimensions from BCFT: O($N$)-symmetric ${\varphi }^{2n}$ theories with a boundary and higher-derivative generalizations
• Mixed phases in feedback Ising models
• The Cubic Fixed Point at Large $N$
• One-dimensional long-range Ising model: two (almost) equivalent approximations
• On the Wilson-Fisher fixed point in the limit of integer spacetime dimensions