Finite-size versus finite-temperature effects in the critical long-range model
arXiv:2311.04607 · doi:10.1007/JHEP02(2024)078
Abstract
In this paper we consider classical and quantum versions of the critical long-range model, for which we study finite-size and finite-temperature effects, respectively, at large . First, we consider the classical (isotropic) model, which is conformally invariant at criticality, and we introduce one compact spatial direction. We show that the finite size dynamically induces an effective mass and we compute the one-point functions for bilinear primary operators with arbitrary spin and twist. Second, we study the quantum model, mapped to a Euclidean anisotropic field theory, local in Euclidean time and long-range in space, which we dub \emph{fractional Lifshitz field theory}. We show that this model admits a fixed point at zero temperature, where it displays anisotropic Lifshitz scaling, and show that at finite temperature a thermal mass is induced. We then compute the one-point functions for an infinite family of bilinear scaling operators. In both the classical and quantum model, we find that, as previously noted for the short-range model in [arXiv:1802.10266], the large- two-point function contains information about the one-point functions, not only of the bilinear operators, but also of operators that appear in the operator product expansion of two fundamental fields only at subleading order in , namely powers of the Hubbard-Stratonovich intermediate field.
arXiv comment37 pages, 4 figures, minor improvements and additional references
References in corpus (34)
- Statistical mechanics and dynamics of solvable models with long-range interactions
- Ten equivalent definitions of the fractional Laplace operator
- Quantum Field Theory in the Large N Limit: a review
- Convexity and Liberation at Large Spin
- Topological Order and Conformal Quantum Critical Points
- SCHRÖdinger Invariance and Strongly Anisotropic Critical Systems
- A universal result on central charges in the presence of double-trace deformations
- Unitarity and the Holographic S-Matrix
- A spacetime derivation of the Lorentzian OPE inversion formula
- The quantum phase transition in the sub-ohmic spin-boson model: Quantum Monte-Carlo study with a continuous imaginary time cluster algorithm
- Renormalization of Lorentz violating theories
- -dimensional SYK, AdS Loops, and Symbols
- A scaling theory for the long-range to short-range crossover and an infrared duality
- Conformal Invariance in the Long-Range Ising Model
- Local scale invariance and strongly anisotropic equilibrium critical systems
- The Conformal Bootstrap at Finite Temperature
- Criticality and Phase Diagram of Quantum Long-Range models
- Long-range critical exponents near the short-range crossover
- Harmonic Analysis and Mean Field Theory
- Polylogarithm Identities in a Conformal Field Theory in Three Dimensions
- Projectors and seed conformal blocks for traceless mixed-symmetry tensors
- The crossover region between long-range and short-range interactions for the critical exponents
- A Complete Renormalization Group Trajectory Between Two Fixed Points
- CRITICAL (Phi^{4}_{3,ε})
- Models with Boundary Interactions and their Long Range Generalizations
- Anisotropic Long-Range Spin Systems
- Critical exponents for long-range O(n) models below the upper critical dimension
- Finite-temperature critical behavior of long-range quantum Ising models
- Dynamics of Finite-Temperature CFTs from OPE Inversion Formulas
- Critical two-point function for long-range models below the upper critical dimension
- Long-range multi-scalar models at three loops
- Gentle introduction to rigorous Renormalization Group: a worked fermionic example
- Finite-temperature critical behaviors in 2D long-range quantum Heisenberg model
- Finite-Size Effects and Operator Product Expansions in a CFT for d>2