Relations between Short Range and Long Range Ising models

Abstract

We perform a numerical study of the long range (LR) ferromagnetic Ising model with power law decaying interactions ($J\propto r^{-d-\sigma }$) both on a one-dimensional chain ($d=1$) and on a square lattice ($d=2$). We use advanced cluster algorithms to avoid the critical slowing down. We first check the validity of the relation connecting the critical behavior of the LR model with parameters $(d,\sigma )$ to that of a short range (SR) model in an equivalent dimension $D$. We then study the critical behavior of the $d=2$ LR model close to the lower critical $\sigma$, uncovering that the spatial correlation function decays with two different power laws: the effect of the subdominant power law is much stronger than finite size effects and actually makes the estimate of critical exponents very subtle. By including this subdominant power law, the numerical data are consistent with the standard renormalization group (RG) prediction by Sak, thus making not necessary (and unlikely, according to Occam's razor) the recent proposal by Picco of having a new set of RG fixed points, in addition to the mean-field one and the SR one.

25 pages, 8 figures

References in corpus (3)

• Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses
• The correspondence between long-range and short-range spin glasses
• Nonlinear Aspects of the Renormalization Group Flows of Dyson's Hierarchical Model

Cited by in corpus (86)

• Long-range interacting quantum systems
• A scaling theory for the long-range to short-range crossover and an infrared duality
• Conformal Invariance in the Long-Range Ising Model
• Criticality and Phase Diagram of Quantum Long-Range $\text{O(N)}$ models
• Fixed Points Structure & Effective Fractional Dimension for O(N) Models with Long-Range Interactions
• Critical and maximally informative encoding between neural populations in the retina
• Causality and quantum criticality in long-range lattice models
• Critical exponents of O(N) models in fractional dimensions
• The crossover region between long-range and short-range interactions for the critical exponents
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Fidelity and criticality of quantum Ising chain with long-range interactions
• Bootstrapping the long-range Ising model in three dimensions
• Fidelity Susceptibility Study of Quantum Long-Range Antiferromagnetic Ising Chain
• Criticality of Spin Systems with Weak Long-Range Interactions
• Upper and Lower Critical Decay Exponents of Ising Ferromagnets with Long-range Interaction
• Quantum Kibble-Zurek physics in long-range transverse-field Ising models
• Random transverse-field Ising chain with long-range interactions
• Quantum quench in long-range field theories
• Dissipative time crystals with long-range Lindbladians
• Dynamical Phase Diagram of a Quantum Ising Chain with Long Range Interactions
• One-dimensional long-range percolation: a numerical study
• Finite-size scaling above the upper critical dimension in Ising models with long-range interactions
• $O(N)$ Models with Boundary Interactions and their Long Range Generalizations
• O(N) and O(N) and O(N)
• Finite-temperature critical behavior of long-range quantum Ising models
• Anisotropic Long-Range Spin Systems
• Quantum criticality and excitations of a long-range anisotropic $XY$-chain in a transverse field
• Long-range random transverse-field Ising model in three dimensions
• Long-range multi-scalar models at three loops
• Universality class of Ising critical states with long-range losses
• Complex networks with tuneable dimensions as a universality playground
• Gauge Theories with Ultracold Atoms
• Gentle introduction to rigorous Renormalization Group: a worked fermionic example
• Unexpected upper critical dimension for spin glass models in a field predicted by the loop expansion around the Bethe solution at zero temperature
• Zero-Temperature Coarsening in the Two-Dimensional Long-Range Ising Model
• Ising model description of long range correlations in DNA sequences
• A model of persistent breaking of discrete symmetry
• Long-range epidemic spreading in a random environment
• Topological edge modes and phase transition in the critical fermionic chain with long-range interaction
• Inverse design of disordered stealthy hyperuniform spin chains
• Turing-like patterns in an asymmetric dynamic Ising model
• Ising chains with competing interactions in presence of long-range couplings
• Cluster Monte Carlo and dynamical scaling for long-range interactions
• Meta-stable states in the hierarchical Dyson model drive parallel processing in the hierarchical Hopfield network
• Analytic and numerical bootstrap for the long-range Ising model
• The low-temperature phase in the two-dimensional long-range diluted XY model
• Ensemble inequivalence in long-range quantum systems
• Self-consistent harmonic approximation with non-local couplings
• The one-dimensional Long-Range Falikov-Kimball Model: Thermal Phase Transition and Disorder-Free Localisation
• Open Quantum Rotors: Connecting Correlations and Physical Currents
• Quantum criticality of a ${\mathbb{Z}}_3$ symmetric spin chain with long-range interactions
• Critical two-point function for long-range models with power-law couplings: The marginal case for $d\ge d_c$
• Phase-transitions of the random bond Potts chain with long-range interactions
• Infinite volume extrapolation in the one-dimensional bond diluted Levy spin-glass model near its lower critical dimension
• Non-universality of aging during phase separation of the two-dimensional long-range Ising model
• Two-dimensional XY Ferromagnet Induced by Long-range Interaction
• Villain model with long-range couplings
• Universality in long-range interacting systems: the effective dimension approach
• Frustration Elimination and Excited State Search in Coherent Ising Machines
• Universal scaling in real dimension
• Universal work statistics in long-range interacting quantum systems
• Transverse-field $XY$ spin chain with the competing long-range interactions: Multi-criticality around the $XX$-symmetric point
• Neural-network quantum state study of the long-range antiferromagnetic Ising chain
• The Nonclassical Regime of the Two-dimensional Long-range XY Model: a Comprehensive Monte Carlo Study
• Optimal spatial searches with long-range tunneling
• Critical exponents of the spin glass transition in a field at zero temperature
• Theory of Critical Phenomena with Long-Range Temporal Interaction
• Critical dynamics of long range models on Dynamical Lévy Lattices
• Addendum: Long-range multi-scalar models at three loops
• Strain Fields and Critical Phenomena in Manganites I: Spin-Lattice Hamiltonians
• Stochastic parameter optimization analysis of dynamical quantum critical phenomena in long-range transverse-field Ising chain
• 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
• Long-range interactions from $U\left(1\right)$ gauge fields via dimensional mismatch
• Persistence discontinuity in disordered contact processes with long-range interactions
• Statistical mechanics of the spherical hierarchical model with random fields
• Fidelity-mediated analysis of the transverse-field $XY$ chain with the long-range interactions: Anisotropy-driven multi-criticality
• Renormalization theory of disordered contact processes with heavy-tailed dispersal
• Criticality of the Higgs mass for the long-range quantum $XY$ chain: Amplitude ratio between the Higgs and paramagnetic gaps
• Ensemble Inequivalence in Long-Range Quantum Spin Systems
• Localized magnetic moments in a Dirac semimetal as a spin model with long--range interactions
• Persistence of the Berezinskii-Kosterlitz-Thouless transition with long-range couplings
• Mixed phases in feedback Ising models
• Criticality of the magnon-bound-state hierarchy for the quantum Ising chain with the long-range interactions
• Berezinskii-Kosterlitz-Thouless phase transitions with long-range couplings
• Strain Fields and Critical Phenomena in Manganites II: Spin-Lattice-Energy Hamiltonians
• One-dimensional long-range Ising model: two (almost) equivalent approximations