Self-Consistent Scaling Theory for Logarithmic Correction Exponents

Abstract

Multiplicative logarithmic corrections frequently characterize critical behaviour in statistical physics. Here, a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when the leading specific-heat critical exponent vanishes. Also, the theory is widened to encompass the correlation function. The new relations are then confronted with results from the literature and some new predictions for logarithmic corrections in certain models are made.

4 pages, to appear in Phys.Rev.Lett

References in corpus (32)

• Classical critical behavior of spin models with long-range interactions
• Lack of Self-Averaging in Critical Disordered Systems
• Logarithmic Corrections and Finite-Size Scaling in the Two-Dimensional 4-State Potts Model
• Scaling Relations for Logarithmic Corrections
• Renormalization Group Analysis of Finite-Size Scaling in the ${\Phi }_4^4$ Model
• Ising exponents in the two-dimensional site-diluted Ising model
• Critical behaviour of the Random--Bond Ashkin--Teller Model, a Monte-Carlo study
• The Structure, Dynamics and Electronic Structure of Liquid Ag-Se Alloys Investigated by Ab Initio Simulation
• 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
• Complex-Temperature Properties of the Ising Model on 2D Heteropolygonal Lattices
• Finite Size Scaling for O(N) phi^4-Theory at the Upper Critical Dimension
• Specific heat of two-dimensional diluted magnets
• Scaling and Density of Lee-Yang Zeroes in the Four Dimensional Ising Model
• On weak vs. strong universality in the two-dimensional random-bond Ising ferromagnet
• Critical Point Correlation Function for the 2D Random Bond Ising Model
• 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
• Transfer-matrix scaling from disorder-averaged correlation lengths for diluted Ising systems
• Critical region of the random bond Ising model
• Logarithmic Corrections for Spin Glasses, Percolation and Lee-Yang Singularities in Six Dimensions
• Correlation decay and conformal anomaly in the two-dimensional random-bond Ising ferromagnet
• 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
• Logarithmic corrections to scaling in critical percolation and random resistor networks
• Logarithmic corrections to gap scaling in random-bond Ising strips
• Logarithmic corrections to correlation decay in two-dimensional random-bond Ising systems
• Fisher Zeroes and Singular Behaviour of the Two Dimensional Potts Model in the Thermodynamic Limit
• Numerical investigation of logarithmic corrections in two-dimensional spin models
• Correlation length-exponent relation for the two-dimensional random Ising model
• Kuehn and Mazzeo Reply

Cited by in corpus (37)

• Anomalous diffusion: A basic mechanism for the evolution of inhomogeneous systems
• Hyperscaling above the upper critical dimension
• Universal dependence on disorder of 2D randomly diluted and random-bond +-J Ising models
• 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
• Absence of logarithmic scaling in the ageing behaviour of the 4D spherical model
• Analytic Partition Function Zeros of the Wako-Saito-Munoz-Eaton beta-hairpin Model
• Phase transitions in the Potts model on complex networks
• 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
• Entropic equation of state and scaling functions near the critical point in scale-free 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
• Quantum phase transitions with dynamical flavors
• Revisiting (logarithmic) scaling relations using renormalization group
• The Site-Diluted Ising Model in Four Dimension
• Universal Amplitude Ratios in the Ising Model in Three Dimensions
• Critical behavior of the 2D Ising model modulated by the Octonacci sequence
• Logarithmic Finite-Size Scaling of the Four-Dimensional Ising Model
• Scaling behaviour of lattice animals at the upper critical dimension
• Scaling functions and amplitude ratios for the Potts model on an uncorrelated scale-free network
• Yang-Lee zeros for real-space condensation
• Phase transitions above the upper critical dimension
• A Microcanonical Inflection Point Analysis via Parametric Curves and its Relation to the Zeros of the Partition Function