Criticality of Spin Systems with Weak Long-Range Interactions

Abstract

The study of critical properties of systems with long-range interactions has attracted in the last decades a continuing interest and motivated the development of several analytical and numerical techniques, in particular in connection with spin models. From the point of view of the investigation of their criticality, a special role is played by systems in which the interactions are long-range enough that their universality class is different from the short-range case and, nevertheless, they maintain the extensivity of thermodynamical quantities. Such interactions are often called weak long-range. In this paper we focus on the study of the critical behaviour of spin systems with weak-long range couplings using renormalization group, and we review their remarkable properties. For the sake of clarity and self-consistency, we start from the classical $O(N)$ spin models and we then move to quantum spin systems.

24 pages, 5 figures, Submitted to the special issue of J. Phys. A on 'Long-range Interactions and Synchronization'

References in corpus (26)

• Many-Body Physics with Ultracold Gases
• Exact evolution equation for the effective potential
• Statistical mechanics and dynamics of solvable models with long-range interactions
• Bose-Einstein Condensation of Erbium
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Observation of mesoscopic crystalline structures in a two-dimensional Rydberg gas
• Quantum degenerate dipolar Fermi gas
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Entanglement entropy for the long range Ising chain
• Kitaev chains with long-range pairing
• Nearly-linear light cones in long-range interacting quantum systems
• Measuring the dynamic structure factor of a quantum gas undergoing a structural phase transition
• Order-N Cluster Monte Carlo Method for Spin Systems with Long-range Interactions
• Critical phenomena and quantum phase transition in long range Heisenberg antiferromagnetic chains
• Critical exponents of O(N) models in fractional dimensions
• The crossover region between long-range and short-range interactions for the critical exponents
• Long-range Heisenberg models in quasi-periodically driven crystals of trapped ions
• Non-equilibrium Phase Transitions with Long-Range Interactions
• Scaling Solutions in Continuous Dimension
• The correspondence between long-range and short-range spin glasses
• Explicit Hamiltonians Inducing Volume Law for Entanglement Entropy in Fermionic Lattices
• Quantum quench in long-range field theories
• Anisotropic Long-Range Spin Systems
• Quantum criticality in spin chains with non-ohmic dissipation
• Nonperturbative renormalization group treatment of amplitude fluctuations for $|\phi {|}^4$ topological phase transitions
• New Anomalous Lieb-Robinson Bounds in Quasi-Periodic XY Chains

Cited by in corpus (40)

• The nonperturbative functional renormalization group and its applications
• Long-range interacting quantum systems
• Out-of-equilibrium phase diagram of long-range superconductors
• Metastability and discrete spectrum of long-range systems
• Quantum criticality and excitations of a long-range anisotropic $XY$-chain in a transverse field
• $BKT$ transitions in classical and quantum long-range systems
• Long-range multi-scalar models at three loops
• Dynamical quantum phase transition in a bosonic system with long-range interactions
• Coexistence of coarsening and mean field relaxation in the long-range Ising chain
• Monte Carlo based techniques for quantum magnets with long-range interactions
• Emergent self-duality in long range critical spin chain: from deconfined criticality to first order transition
• Self-consistent harmonic approximation with non-local couplings
• Ensemble inequivalence in long-range quantum systems
• Mutual information for fermionic systems
• Domain statistics in the relaxation of the one-dimensional Ising model with strong long-range interactions
• Kinetics of the one-dimensional voter model with long-range interactions
• Survival in two-species reaction-superdiffusion system: Renormalization group treatment and numerical simulations
• Finite Temperature Off-Diagonal Long-Range Order for Interacting Bosons
• Simulating long-range hopping with periodically-driven superconducting qubits
• Villain model with long-range couplings
• Entanglement propagation and dynamics in non-additive quantum systems
• Quantum phases of hardcore bosons with repulsive dipolar density-density interactions on two-dimensional lattices
• Universality in long-range interacting systems: the effective dimension approach
• Universal cooling dynamics toward a quantum critical point
• Effective-Dimension Theory of Critical Phenomena above Upper Critical Dimensions
• Critical phase induced by Berry phase and dissipation in a spin chain
• Universal scaling in real dimension
• Theory of Critical Phenomena with Long-Range Temporal Interaction
• Neural-network quantum state study of the long-range antiferromagnetic Ising chain
• On the new universality class in structurally disordered $n$-vector model with long-range interactions
• Entanglement of weighted graphs uncovers transitions in variable-range interacting models
• Nonperturbative treatment of a quenched Langevin field theory
• Fractional Dynamics and Modulational Instability in Long-Range Heisenberg Chains
• RG studies of scalar-field models of long-range interactions
• Ensemble Inequivalence in Long-Range Quantum Spin Systems
• One-dimensional long-range Ising model: two (almost) equivalent approximations
• Preface: Long-range Interactions and Synchronization
• Berezinskii-Kosterlitz-Thouless phase transitions with long-range couplings
• The Lattice Schwinger Model and Its Quantum Simulation
• Critical exponents of the Ising model with quenched structural disorder and long-range interactions at spatial dimension $d=3$