Finite size scaling of the correlation length above the upper critical dimension

Abstract

We show numerically that correlation length at the critical point in the five-dimensional Ising model varies with system size L as L^{5/4}, rather than proportional to L as in standard finite size scaling (FSS) theory. Our results confirm a hypothesis that FSS expressions in dimension d greater than the upper critical dimension of 4 should have L replaced by L^{d/4} for cubic samples with periodic boundary conditions. We also investigate numerically the logarithmic corrections to FSS in d = 4.

arXiv comment5 pages, 6 postscript figures

References in corpus (5)

• Finite-size Scaling and Universality above the Upper Critical Dimensionality
• Finite-size scaling above the upper critical dimension revisited: The case of the five-dimensional Ising model
• Universality and the five-dimensional Ising model
• Lattice ${\varphi }^4$ theory of finite-size effects above the upper critical dimension
• Cutoff and lattice effects in the $\varphy^4$ theory of confined systems

Cited by in corpus (40)

• Realization of the mean-field universality class in spin-crossover materials
• On the path integral representation for quantum spin models and its application to the quantum cavity method and to Monte Carlo simulations
• Hyperscaling above the upper critical dimension
• Finite-size scaling above the upper critical dimension
• Critical behavior and synchronization of discrete stochastic phase coupled oscillators
• Finite-size scaling above the upper critical dimension in Ising models with long-range interactions
• Numerical studies of a one-dimensional 3-spin spin-glass model with long-range interactions
• Fisher's scaling relation above the upper critical dimension
• Finite size scaling of the 5D Ising model with free boundary conditions
• Critical behavior of the Random-Field Ising model at and beyond the Upper Critical Dimension
• A new critical exponent koppa and its logarithmic counterpart koppa-hat
• Scaling at quantum phase transitions above the upper critical dimension
• Predictive power of MCT: Numerics and Finite size scaling for a mean field spin glass
• Random Transverse Field Ising Model in dimension $d>1$ : scaling analysis in the disordered phase from the Directed Polymer model
• One-dimensional infinite component vector spin glass with long-range interactions
• Finite-size critical scaling in Ising spin glasses in the mean-field regime
• Monte Carlo based techniques for quantum magnets with long-range interactions
• Phase Transitions in the 1-d Long-Range Diluted Heisenberg Spin Glass
• Extended Scaling in High Dimensions
• Spin glasses in the non-extensive regime
• Study of the de Almeida-Thouless line using one-dimensional power-law diluted Heisenberg Spin Glasses
• Finite-size scaling of the random-field Ising model above the upper critical dimension
• Complete graph and Gaussian fixed point asymptotics in the five-dimensional Fortuin-Kasteleyn Ising model with periodic boundaries
• Exact ground states of one-dimensional long-range random-field Ising magnets
• Random field Ising model : statistical properties of low-energy excitations and of equilibrium avalanches
• Triviality problem and the high-temperature expansions of the higher susceptibilities for the Ising and the scalar field models on four-, five- and six-dimensional lattices
• Logarithmic finite-size scaling of the self-avoiding walk at four dimensions
• Complete graph asymptotics for the Ising and random cluster models on 5D grids with cyclic boundary
• Finite-size scaling of the d=5 Ising model embedded in the cylindrical geometry: An influence of the hyperscaling violation
• Finite-Size Scaling for Quantum Criticality above the Upper Critical Dimension: Superfluid-Mott-Insulator Transition in Three Dimensions
• Effective-Dimension Theory of Critical Phenomena above Upper Critical Dimensions
• Excitations in high-dimensional random-field Ising magnets
• Transverse-field $XY$ spin chain with the competing long-range interactions: Multi-criticality around the $XX$-symmetric point
• Theory of Critical Phenomena with Long-Range Temporal Interaction
• Static and dynamical magnetic properties of the extended Kitaev-Heisenberg model with spin vacancies
• When correlations exceed system size: finite-size scaling in free boundary conditions above the upper critical dimension
• Phase transitions above the upper critical dimension
• Finite-Size Scaling of the majority-voter model above the upper critical dimension
• Non-Commutative weak measurements: Entanglement, Symmetry Breaking, and the Role of Readout
• The Ising ferromagnet in dimension five: link and spin overlaps