Scaling Relations for Logarithmic Corrections

Abstract

Multiplicative logarithmic corrections to scaling are frequently encountered in the critical behavior of certain statistical-mechanical systems. Here, a Lee-Yang zero approach is used to systematically analyse the exponents of such logarithms and to propose scaling relations between them. These proposed relations are then confronted with a variety of results from the literature.

4 pages

References in corpus (20)

• Classical critical behavior of spin models with long-range interactions
• Logarithmic Corrections and Finite-Size Scaling in the Two-Dimensional 4-State Potts Model
• Renormalization Group Analysis of Finite-Size Scaling in the ${\Phi }_4^4$ Model
• Simulations of lattice animals and trees
• Critical Behaviour of the Randomly Spin--Diluted 2-d Ising Model --- A Grand Ensemble Approach
• Critical behaviour of the 2d spin diluted Ising model via the equilibrium ensemble approach
• Finite Size Scaling for O(N) phi^4-Theory at the Upper Critical Dimension
• Specific heat of two-dimensional diluted magnets
• On weak vs. strong universality in the two-dimensional random-bond Ising ferromagnet
• Critical behavior of weakly-disordered anisotropic systems in two dimensions
• High-Temperature Series Analysis of the Free Energy and Susceptibility of the 2D Random-Bond Ising Model
• Critical region of the random bond Ising model
• Logarithmic Corrections for Spin Glasses, Percolation and Lee-Yang Singularities in Six Dimensions
• Fermionic Structure of Two-Dimensional Ising Model with Quenched Site Dilution
• Comment on: Critical behavior on the spin diluted 2D Ising model: A grand ensemble approach, by R. Kuehn
• Scaling and finte-size-scaling in the two dimensional random-coupling Ising ferromagnet
• Universal finite-size scaling analysis of Ising models with long-range interactions at the upper critical dimensionality: Isotropic case
• Number of spanning clusters at the high-dimensional percolation thresholds
• Numerical investigation of logarithmic corrections in two-dimensional spin models
• Kuehn and Mazzeo Reply

Cited by in corpus (47)

• Hyperscaling above the upper critical dimension
• Self-Consistent Scaling Theory for Logarithmic Correction Exponents
• Fisher's scaling relation above the upper critical dimension
• Exact Partition Function Zeros of the Wako-Saito-Muñoz-Eaton Protein Model
• Exact Partition Function Zeros of a Polymer on a Simple-Cubic Lattice
• Scaling Analysis of the Site-Diluted Ising Model in Two Dimensions
• A new critical exponent koppa and its logarithmic counterpart koppa-hat
• Quenched bond randomness in marginal and non-marginal Ising spin models in 2D
• Logarithmic finite-size scaling correction to the leading Fisher zeros in the p-state clock model: A higher-order tensor renormalization group study
• Quantum phase transition in the spin-anisotropic quantum spherical model
• Critical behavior of the pure and random-bond two-dimensional triangular Ising ferromagnet
• Critical amplitude ratios of the Baxter-Wu model
• Universality aspects of the 2d random-bond Ising and 3d Blume-Capel models
• Critical phenomena on scale-free networks: logarithmic corrections and scaling functions
• Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws
• Analytic Partition Function Zeros of the Wako-Saito-Munoz-Eaton beta-hairpin Model
• Absence of logarithmic scaling in the ageing behaviour of the 4D spherical model
• Phase transitions in the Potts model on complex networks
• Ferromagnetic Potts models with multisite interaction
• Critical and tricritical behavior of the $d=3$ Blume-Capel model: Results from small-scale Monte Carlo simulations
• Universality of the Ising and the S=1 model on Archimedean lattices: A Monte Carlo determination
• Tensor network calculation of the logarithmic correction exponent in the XY model
• The two-dimensional 4-state Potts model in a magnetic field
• Entropic equation of state and scaling functions near the critical point in scale-free networks
• Apparent universality of $1/f$ spectra as an artifact of finite-size effects
• The Diffusive Epidemic Process on Barabasi-Albert Networks
• Microcanonical finite-size scaling in specific heat diverging 2nd order phase transitions
• Fisher Renormalization for Logarithmic Corrections
• Exactly solvable models of growing interfaces and lattice gases: the Arcetri models, ageing and logarithmic sub-ageing
• A comparative study of the dynamic critical behavior of the four-state Potts like models
• Quantum phase transitions with dynamical flavors
• Revisiting (logarithmic) scaling relations using renormalization group
• Evidence of a second-order phase transition in the six-dimensional Ising spin glass in a field
• The Site-Diluted Ising Model in Four Dimension
• Universal Amplitude Ratios in the Ising Model in Three Dimensions
• Absorbing phase transitions in a non-conserving sandpile model
• Revisiting the Lee-Yang singularities in the four-dimensional Ising model: a tribute to the memory of Ralph Kenna
• Critical behavior of the 2D Ising model modulated by the Octonacci sequence
• Scaling behaviour of lattice animals at the upper critical dimension
• Numerical study of the overlap Lee-Yang singularities in the three-dimensional Edwards-Anderson model
• Logarithmic Finite-Size Scaling of the Four-Dimensional Ising Model
• Scaling functions and amplitude ratios for the Potts model on an uncorrelated scale-free network
• A Microcanonical Inflection Point Analysis via Parametric Curves and its Relation to the Zeros of the Partition Function
• Yang-Lee zeros for real-space condensation
• Phase transitions above the upper critical dimension
• Long-range correlations with finite-size effects from a superposition of uncorrelated pulses with power-law distributed durations
• On a previously unpublished work with Ralph Kenna